lab1 tutorial.sagews

#lab 1 tutorial

#plotting
#interactives
#animations
#solving a differential equation

var('x')

x

var('N')
N+N+N+N

N 4*N

f(x) = 5*x^3
f(1)

5

plot(f, (x, -5,5), color="red", axes_labels=['x','f(x)'])

@interact
def plot_this(a = (-2,2,1), b = (0,5), c=1):
    G(N) = a*N^2 + b*c
    p = plot(G)
    show(p)

Interact: please open in CoCalc

@interact
def plot_this_thing(a=(0,5,1), n=(0,3), b=1):
    f(x) = a*x^3 + b
    p = plot(f, (x, -5,5), color="red", axes_labels=['x','f(x)'])
    show(p)

Interact: please open in CoCalc

# animations

frames = []
for i in srange(0,10):
    p = plot(sin(i*x), (x,0,5))
    frames.append(p)
movie = animate(frames)
show(movie, gif=True)

# animations
frames = []
for i in srange(10):
    p = plot(sin(i*x), (x,0,5))
    frames.append(p)
movie = animate(frames)
show(movie, gif=True)

# differential equations
#1 setup
#2 desolve_odeint
#3 view results (time series or trajectory)

# setup

# romeo and juliet
var('R')
var('J')

DEs = [-.5*R + J, -J  ] # R' is 1st, J' is 2nd

ic = [1,2]

t = srange(0,100,.1)

R J

# solving the DE

sol = desolve_odeint(DEs, dvars=[R,J], ics=ic, times=t)

sol

array([[ 1.00000000e+00, 2.00000000e+00], [ 1.13679743e+00, 1.80967485e+00], [ 1.24926408e+00, 1.63746151e+00], ..., [ -2.56445412e-11, -5.44200397e-15], [ -2.55186523e-11, -5.41390943e-15], [ -2.53927634e-11, -5.38581490e-15]])

# visualize data

#trajectory
list_plot(sol)

# time series
zip(t,sol[:,0])

[(0.000000000000000, 1.0), (0.100000000000000, 1.1367974279197288), (0.200000000000000, 1.2492640787088778), (0.300000000000000, 1.3402669761409833), (0.400000000000000, 1.4123735511366169), (0.500000000000000, 1.4678812446817815), (0.600000000000000, 1.5088445109732522), (0.700000000000000, 1.5370991890403891), (0.800000000000000, 1.5542843612930173), (0.900000000000000, 1.5618621189131143), (1.00000000000000, 1.5611355359869399), (1.10000000000000, 1.5532647227947791), (1.20000000000000, 1.539281340115378), (1.30000000000000, 1.5201017211138705), (1.40000000000000, 1.4965386828224501), (1.50000000000000, 1.4693121458683605), (1.60000000000000, 1.4390587733584881), (1.70000000000000, 1.4063405910498779), (1.80000000000000, 1.3716527763068278), (1.90000000000000, 1.3354306721271119), (2.00000000000000, 1.2980561045264496), (2.10000000000000, 1.2598630641278872), (2.20000000000000, 1.221142816996907), (2.30000000000000, 1.1821485075065716), (2.40000000000000, 1.1430992774173752), (2.50000000000000, 1.104184007806789), (2.60000000000000, 1.0655646637737701), (2.70000000000000, 1.0273792606736767), (2.80000000000000, 0.98974457581994901), (2.90000000000000, 0.95275856594265851), (3.00000000000000, 0.91650253177582641), (3.10000000000000, 0.88104306393943133), (3.20000000000000, 0.84643377783169071), (3.30000000000000, 0.81271687621111577), (3.40000000000000, 0.77992454238173414), (3.50000000000000, 0.74808018478572957), (3.60000000000000, 0.71719954981142087), (3.70000000000000, 0.68729172382862269), (3.80000000000000, 0.65836000556234953), (3.90000000000000, 0.63040270930280506), (4.00000000000000, 0.60341385685762616), (4.10000000000000, 0.5773838127498917), (4.20000000000000, 0.55229982965966795), (4.30000000000000, 0.52814654891623303), (4.40000000000000, 0.50490642816629139), (4.50000000000000, 0.48256013280756005), (4.60000000000000, 0.46108687155875344), (4.70000000000000, 0.44046469880466188), (4.80000000000000, 0.42067077444732359), (4.90000000000000, 0.40168159661846875), (5.00000000000000, 0.38347320165927534), (5.10000000000000, 0.36602134029297251), (5.20000000000000, 0.34930163002370851), (5.30000000000000, 0.3332896865023951), (5.40000000000000, 0.31796123699071799), (5.50000000000000, 0.30329221743989554), (5.60000000000000, 0.28925885559177511), (5.70000000000000, 0.27583773997821359), (5.80000000000000, 0.26300587893967436), (5.90000000000000, 0.25074074823877512), (5.99999999999999, 0.23902033110020215), (6.09999999999999, 0.22782314911092644), (6.19999999999999, 0.21712828762570208), (6.29999999999999, 0.20691541353094189), (6.39999999999999, 0.19716478927623496), (6.49999999999999, 0.18785728093539977), (6.59999999999999, 0.17897436348476378), (6.69999999999999, 0.17049812118837226), (6.79999999999999, 0.16241124750670127), (6.89999999999999, 0.15469703867074475), (6.99999999999999, 0.14733938800507088), (7.09999999999999, 0.14032277794852316), (7.19999999999999, 0.13363226894196878), (7.29999999999999, 0.12725348888147422), (7.39999999999999, 0.12117262170189966), (7.49999999999999, 0.11537639208355345), (7.59999999999999, 0.10985205402680201), (7.69999999999999, 0.10458737381248272), (7.79999999999999, 0.099570617762223937), (7.89999999999999, 0.094790535049588925), (7.99999999999999, 0.090236344226428941), (8.09999999999999, 0.085897716850409436), (8.19999999999999, 0.081764762881944258), (8.29999999999999, 0.07782801523546666), (8.39999999999999, 0.074078414838801038), (8.49999999999999, 0.070507296073815798), (8.59999999999999, 0.067106371786396793), (8.69999999999999, 0.063867719524969349), (8.79999999999998, 0.060783767057088364), (8.89999999999998, 0.057847279206994735), (8.99999999999998, 0.055051343566599374), (9.09999999999998, 0.052389359053259837), (9.19999999999998, 0.049855021969539552), (9.29999999999998, 0.047442313745589909), (9.39999999999998, 0.045145491126325488), (9.49999999999998, 0.042959071058371781), (9.59999999999998, 0.040877823517978903), (9.69999999999998, 0.038896757929613349), (9.79999999999998, 0.037011113499943571), (9.89999999999998, 0.035216351350377643), (9.99999999999998, 0.033508140982334213), (10.1000000000000, 0.031882355315885555), (10.2000000000000, 0.030335058395525902), (10.3000000000000, 0.028862498434371966), (10.4000000000000, 0.027461100350054651), (10.5000000000000, 0.026127454574401382), (10.6000000000000, 0.024858314334313764), (10.7000000000000, 0.023650584680618678), (10.8000000000000, 0.02250131609972221), (10.9000000000000, 0.021407700476996139), (11.0000000000000, 0.020367060432958009), (11.1000000000000, 0.019376847080567521), (11.2000000000000, 0.018434632378155926), (11.3000000000000, 0.017538102548620888), (11.4000000000000, 0.016685055967927548), (11.5000000000000, 0.015873394357874968), (11.6000000000000, 0.01510111991462933), (11.7000000000000, 0.014366331287808926), (11.8000000000000, 0.013667216498002878), (11.9000000000000, 0.013002052540205424), (12.0000000000000, 0.01236919750505406), (12.1000000000000, 0.011767086810155272), (12.2000000000000, 0.011194230595755177), (12.3000000000000, 0.010649212950195584), (12.4000000000000, 0.010130685964573666), (12.5000000000000, 0.0096373683549807795), (12.6000000000000, 0.009168039408978949), (12.7000000000000, 0.0087215334307074698), (12.8000000000000, 0.0082967438672647206), (12.9000000000000, 0.0078926184210444689), (13.0000000000000, 0.0075081542806606982), (13.1000000000000, 0.0071423963611093556), (13.2000000000000, 0.0067944366779426396), (13.3000000000000, 0.006463411425158383), (13.4000000000000, 0.006148497834848856), (13.5000000000000, 0.0058489130249000914), (13.6000000000000, 0.0055639123480862931), (13.7000000000000, 0.0052927873576981586), (13.8000000000000, 0.0050348632926513343), (13.9000000000000, 0.0047894983351844528), (14.0000000000000, 0.0045560819934204041), (14.1000000000000, 0.004334033409317809), (14.2000000000000, 0.0041227994522028619), (14.3000000000000, 0.0039218541450632624), (14.4000000000000, 0.0037306972385936846), (14.5000000000000, 0.0035488526046145428), (14.6000000000000, 0.0033758667867581833), (14.7000000000000, 0.0032113086193427736), (14.8000000000000, 0.0030547679291605899), (14.9000000000000, 0.0029058543840486018), (15.0000000000000, 0.0027641966271546507), (15.1000000000000, 0.0026294415411829038), (15.2000000000000, 0.0025012532441611125), (15.3000000000000, 0.0023793121794806809), (15.4000000000000, 0.0022633137410211774), (15.5000000000000, 0.0021529686530324297), (15.6000000000000, 0.0020480016835337377), (15.7000000000000, 0.0019481507311940225), (15.8000000000000, 0.0018531665421336217), (15.9000000000000, 0.0017628120483631133), (16.0000000000000, 0.0016768617687738039), (16.1000000000000, 0.001595101205614079), (16.2000000000000, 0.0015173262023586358), (16.3000000000000, 0.0014433424536337402), (16.4000000000000, 0.0013729654964400996), (16.5000000000000, 0.0013060195689238087), (16.6000000000000, 0.0012423371503755671), (16.7000000000000, 0.0011817592044778343), (16.8000000000000, 0.001124134754863832), (16.9000000000000, 0.0010693197151786871), (17.0000000000000, 0.001017176884536782), (17.1000000000000, 0.0009675763458366197), (17.2000000000000, 0.00092039423131164578), (17.3000000000000, 0.00087551246952525879), (17.4000000000000, 0.0008328189484527607), (17.5000000000000, 0.00079220721121093542), (17.6000000000000, 0.00075357567420097265), (17.7000000000000, 0.00071682760382114506), (17.8000000000000, 0.00068187141143441748), (17.9000000000000, 0.00064861976539482002), (18.0000000000000, 0.00061698941414755845), (18.1000000000000, 0.00058690132294532762), (18.2000000000000, 0.00055828046189206222), (18.3000000000000, 0.00053105523582567832), (18.4000000000000, 0.0005051574735756751), (18.5000000000000, 0.0004805226081618136), (18.6000000000000, 0.00045708907848840359), (18.7000000000000, 0.00043479819930344638), (18.8000000000000, 0.00041359442677938075), (18.9000000000000, 0.00039342503810205334), (19.0000000000000, 0.00037423955051749168), (19.1000000000000, 0.00035598977296696726), (19.2000000000000, 0.00033862962750409622), (19.3000000000000, 0.00032211531817890037), (19.4000000000000, 0.00030640645692123935), (19.5000000000000, 0.00029146390515401473), (19.6000000000000, 0.00027725020931141698), (19.7000000000000, 0.00026372958792352555), (19.8000000000000, 0.00025086781122637725), (19.9000000000000, 0.00023863308126851186), (20.0000000000000, 0.00022699523064177214), (20.1000000000000, 0.00021592513900177418), (20.2000000000000, 0.00020539500265386303), (20.3000000000000, 0.00019537822968550058), (20.4000000000000, 0.00018584962358121325), (20.5000000000000, 0.00017678588210256064), (20.6000000000000, 0.00016816437028614856), (20.7000000000000, 0.00015996344588613251), (20.8000000000000, 0.00015216241606317131), (20.9000000000000, 0.00014474148848224428), (21.0000000000000, 0.0001376824058963181), (21.1000000000000, 0.00013096771961442895), (21.2000000000000, 0.00012458061430162734), (21.3000000000000, 0.00011850503402682615), (21.4000000000000, 0.00011272562197827097), (21.5000000000000, 0.0001072278884412747), (21.6000000000000, 0.00010199837759346845), (21.7000000000000, 9.7024016741241082e-05), (21.8000000000000, 9.2292321497721881e-05), (21.9000000000000, 8.7791357480006426e-05), (22.0000000000000, 8.3509740373959192e-05), (22.1000000000000, 7.9437076076950829e-05), (22.2000000000000, 7.5563290487122944e-05), (22.3000000000000, 7.1878658408896175e-05), (22.4000000000000, 6.8373865625047516e-05), (22.5000000000000, 6.5039969813463964e-05), (22.6000000000001, 6.1868361463896207e-05), (22.7000000000001, 5.8850875112193845e-05), (22.8000000000001, 5.598052240312481e-05), (22.9000000000001, 5.3250251014877307e-05), (23.0000000000001, 5.0653225922161639e-05), (23.1000000000001, 4.8182911110041837e-05), (23.2000000000001, 4.5833043102527603e-05), (23.3000000000001, 4.3597604491166273e-05), (23.4000000000001, 4.1470934994842002e-05), (23.5000000000001, 3.9448054529661561e-05), (23.6000000000001, 3.7523952085165365e-05), (23.7000000000001, 3.5693809382633871e-05), (23.8000000000001, 3.3953013431145144e-05), (23.9000000000001, 3.2297137127362822e-05), (24.0000000000001, 3.0721919855324112e-05), (24.1000000000001, 2.9223403579507928e-05), (24.2000000000001, 2.7798076205723125e-05), (24.3000000000001, 2.6442376730434922e-05), (24.4000000000001, 2.5152888661837418e-05), (24.5000000000001, 2.3926335049677314e-05), (24.6000000000001, 2.2759564438091661e-05), (24.7000000000001, 2.1649536818445631e-05), (24.8000000000001, 2.0593503633340043e-05), (24.9000000000001, 1.958901111521613e-05), (25.0000000000001, 1.8633550763510126e-05), (25.1000000000001, 1.7724726416922506e-05), (25.2000000000001, 1.6860245952897434e-05), (25.3000000000001, 1.6037911991754745e-05), (25.4000000000001, 1.5255612989615538e-05), (25.5000000000001, 1.4511440552196231e-05), (25.6000000000001, 1.3803610804036945e-05), (25.7000000000001, 1.3130354190250613e-05), (25.8000000000001, 1.2489978326361931e-05), (25.9000000000001, 1.1880861041291501e-05), (26.0000000000001, 1.1301443420339965e-05), (26.1000000000001, 1.0750226154321345e-05), (26.2000000000001, 1.0225887285770621e-05), (26.3000000000001, 9.7271602551218035e-06), (26.4000000000001, 9.2527924919962231e-06), (26.5000000000001, 8.8015845620701744e-06), (26.6000000000001, 8.3723851839256205e-06), (26.7000000000001, 7.9640862459008802e-06), (26.8000000000001, 7.5756259205685022e-06), (26.9000000000001, 7.2060947547394773e-06), (27.0000000000001, 6.8545979141083332e-06), (27.1000000000001, 6.5202568624213215e-06), (27.2000000000001, 6.2022324151581758e-06), (27.3000000000001, 5.8997214265794392e-06), (27.4000000000001, 5.6119534767737909e-06), (27.5000000000001, 5.3379718177224049e-06), (27.6000000000001, 5.0777031522165229e-06), (27.7000000000001, 4.8300879519606842e-06), (27.8000000000001, 4.5945362632008626e-06), (27.9000000000001, 4.3704734296124489e-06), (28.0000000000001, 4.1573400923002479e-06), (28.1000000000001, 3.9545921897984791e-06), (28.2000000000001, 3.7617171218817991e-06), (28.3000000000001, 3.5782790054698882e-06), (28.4000000000001, 3.4038180184453469e-06), (28.5000000000001, 3.2378870591799557e-06), (28.6000000000001, 3.0800576915240236e-06), (28.7000000000001, 2.9299201448063888e-06), (28.8000000000001, 2.7870833138344192e-06), (28.9000000000001, 2.6511747588940105e-06), (29.0000000000001, 2.5218408150352544e-06), (29.1000000000001, 2.3987617292072759e-06), (29.2000000000001, 2.2816381497763147e-06), (29.3000000000001, 2.170181929871106e-06), (29.4000000000001, 2.0641245408383309e-06), (29.5000000000001, 1.9632170722426116e-06), (29.6000000000002, 1.8672302318665126e-06), (29.7000000000002, 1.7759543457105415e-06), (29.8000000000002, 1.6891993579931486e-06), (29.9000000000002, 1.6067654020950139e-06), (30.0000000000002, 1.5283487590607479e-06), (30.1000000000002, 1.4537412248666924e-06), (30.2000000000002, 1.3827607199017314e-06), (30.3000000000002, 1.3152381302035805e-06), (30.4000000000002, 1.2510173074587863e-06), (30.5000000000002, 1.1899550690027266e-06), (30.6000000000002, 1.1319211978196107e-06), (30.7000000000002, 1.0767981208911648e-06), (30.8000000000002, 1.0244054476680971e-06), (30.9000000000002, 9.7456188555356194e-07), (31.0000000000002, 9.2713964388903086e-07), (31.1000000000002, 8.8201899578402446e-07), (31.2000000000002, 8.3908827811611168e-07), (31.3000000000002, 7.9824389153091052e-07), (31.4000000000002, 7.5939030044208762e-07), (31.5000000000002, 7.2244003303135823e-07), (31.6000000000002, 6.8631611451146412e-07), (31.7000000000002, 6.532877863071655e-07), (31.8000000000002, 6.2172252559400598e-07), (31.9000000000002, 5.9158099754507361e-07), (32.0000000000002, 5.6282386733345655e-07), (32.1000000000002, 5.3541180013224272e-07), (32.2000000000002, 5.0930546111452018e-07), (32.3000000000002, 4.8446551545337706e-07), (32.4000000000002, 4.6085257579598844e-07), (32.5000000000002, 4.3840231578045885e-07), (32.6000000000002, 4.1704762970842005e-07), (32.7000000000002, 3.9673891999174735e-07), (32.8000000000002, 3.7742658904231626e-07), (32.9000000000002, 3.5906103927200208e-07), (33.0000000000002, 3.4159267309268027e-07), (33.1000000000002, 3.2497189291622607e-07), (33.2000000000002, 3.0914910115451507e-07), (33.3000000000002, 2.9409158940780036e-07), (33.4000000000002, 2.7978441098802554e-07), (33.5000000000002, 2.6618889420711458e-07), (33.6000000000002, 2.5326593378111071e-07), (33.7000000000002, 2.4097642442605734e-07), (33.8000000000002, 2.2928126085799765e-07), (33.9000000000002, 2.1814133779297499e-07), (34.0000000000002, 2.075175499470326e-07), (34.1000000000002, 1.9738400744688507e-07), (34.2000000000002, 1.8775130264246955e-07), (34.3000000000002, 1.785973116942284e-07), (34.4000000000002, 1.6989679810416889e-07), (34.5000000000002, 1.6162452537429821e-07), (34.6000000000002, 1.5375525700662366e-07), (34.7000000000002, 1.462637565031524e-07), (34.8000000000002, 1.3912478736589173e-07), (34.9000000000002, 1.3101899353945905e-07), (35.0000000000002, 1.2498859868721933e-07), (35.1000000000002, 1.1916761231009995e-07), (35.2000000000002, 1.1355603440810086e-07), (35.3000000000002, 1.0815386498122206e-07), (35.4000000000002, 1.0296110402946358e-07), (35.5000000000002, 9.7977751552825386e-08), (35.6000000000002, 9.3203807551307494e-08), (35.7000000000002, 8.8638155966775939e-08), (35.8000000000002, 8.4260668667960047e-08), (35.9000000000002, 8.0063879851092067e-08), (36.0000000000002, 7.6047789516171948e-08), (36.1000000000002, 7.2212397663199728e-08), (36.2000000000002, 6.8557704292175382e-08), (36.3000000000002, 6.5083709403098922e-08), (36.4000000000002, 6.1790412995970349e-08), (36.5000000000002, 5.8677815070789655e-08), (36.6000000000003, 5.5745915627556848e-08), (36.7000000000003, 5.2994714666271928e-08), (36.8000000000003, 5.0420871559744049e-08), (36.9000000000003, 4.7969930645000868e-08), (37.0000000000003, 4.5622757294514596e-08), (37.1000000000003, 4.3379351508285252e-08), (37.2000000000003, 4.1239713286312821e-08), (37.3000000000003, 3.9203842628597312e-08), (37.4000000000003, 3.7271739535138724e-08), (37.5000000000003, 3.5443404005937057e-08), (37.6000000000003, 3.3718836040992311e-08), (37.7000000000003, 3.2098035640304487e-08), (37.8000000000003, 3.0581002803873583e-08), (37.9000000000003, 2.9165287006988954e-08), (38.0000000000003, 2.7814601469329571e-08), (38.1000000000003, 2.6516869850725825e-08), (38.2000000000003, 2.5272092151177728e-08), (38.3000000000003, 2.4080268370685276e-08), (38.4000000000003, 2.2941398509248468e-08), (38.5000000000003, 2.1855482566867305e-08), (38.6000000000003, 2.0822520543541786e-08), (38.7000000000003, 1.9842512439271913e-08), (38.8000000000003, 1.8915458254057684e-08), (38.9000000000003, 1.80413579878991e-08), (39.0000000000003, 1.7218971546556934e-08), (39.1000000000003, 1.6431543654759123e-08), (39.2000000000003, 1.5673794417450916e-08), (39.3000000000003, 1.4945723834632317e-08), (39.4000000000003, 1.4247331906303325e-08), (39.5000000000003, 1.357861863246394e-08), (39.6000000000003, 1.2939584013114163e-08), (39.7000000000003, 1.2330228048253993e-08), (39.8000000000003, 1.1750550737883431e-08), (39.9000000000003, 1.1200552082002474e-08), (40.0000000000003, 1.0680232080611125e-08), (40.1000000000003, 1.0189590733709383e-08), (40.2000000000003, 9.7230154990325382e-09), (40.3000000000003, 9.2736921467589685e-09), (40.4000000000003, 8.8416050127358506e-09), (40.5000000000003, 8.4267540969631844e-09), (40.6000000000003, 8.0291393994409699e-09), (40.7000000000003, 7.6487609201692072e-09), (40.8000000000003, 7.2856186591478953e-09), (40.9000000000003, 6.9397126163770353e-09), (41.0000000000003, 6.6110427918566261e-09), (41.1000000000003, 6.2996091855866687e-09), (41.2000000000003, 6.0054117975671638e-09), (41.3000000000003, 5.7272914871646286e-09), (41.4000000000003, 5.4599943084431041e-09), (41.5000000000003, 5.2028776652880036e-09), (41.6000000000003, 4.9559415576993262e-09), (41.7000000000003, 4.7191859856770729e-09), (41.8000000000003, 4.4926109492212419e-09), (41.9000000000003, 4.276216448331834e-09), (42.0000000000003, 4.0700024830088493e-09), (42.1000000000003, 3.8739690532522886e-09), (42.2000000000003, 3.6881161590621506e-09), (42.3000000000003, 3.5124438004384358e-09), (42.4000000000003, 3.3468736793594825e-09), (42.5000000000003, 3.1887400739718541e-09), (42.6000000000003, 3.0367354290890017e-09), (42.7000000000003, 2.890859744710924e-09), (42.8000000000003, 2.7511130208376215e-09), (42.9000000000003, 2.617495257469095e-09), (43.0000000000003, 2.4900064546053441e-09), (43.1000000000003, 2.3686466122463683e-09), (43.2000000000003, 2.253415730392168e-09), (43.3000000000003, 2.144313809042743e-09), (43.4000000000003, 2.0413408481980935e-09), (43.5000000000003, 1.9444352905338349e-09), (43.6000000000003, 1.8519892516009805e-09), (43.7000000000004, 1.7632926742580259e-09), (43.8000000000004, 1.6783455585049711e-09), (43.9000000000004, 1.5971479043418164e-09), (44.0000000000004, 1.5196997117685616e-09), (44.1000000000004, 1.4460009807852066e-09), (44.2000000000004, 1.3760517113917516e-09), (44.3000000000004, 1.3098519035881968e-09), (44.4000000000004, 1.2474015573745417e-09), (44.5000000000004, 1.1887006727507866e-09), (44.6000000000004, 1.1336944334104362e-09), (44.7000000000004, 1.0812466696332453e-09), (44.8000000000004, 1.0309055433202233e-09), (44.9000000000004, 9.8267105447137009e-10), (45.0000000000004, 9.3654320308668602e-10), (45.1000000000004, 8.9252198916617104e-10), (45.2000000000004, 8.5060741270982493e-10), (45.3000000000004, 8.1079947371764772e-10), (45.4000000000004, 7.7309817218963958e-10), (45.5000000000004, 7.3750350812580044e-10), (45.6000000000004, 7.0401548152613018e-10), (45.7000000000004, 6.6592078881213009e-10), (45.8000000000004, 6.1289773971404727e-10), (45.9000000000004, 5.6115198470008305e-10), (46.0000000000004, 5.1068352377023692e-10), (46.1000000000004, 4.6149235692450918e-10), (46.2000000000004, 4.1357848416289984e-10), (46.3000000000004, 3.6694190548540901e-10), (46.4000000000004, 3.2158262089203656e-10), (46.5000000000004, 2.7750063038278221e-10), (46.6000000000004, 2.3469593395764646e-10), (46.7000000000004, 1.9316853161662931e-10), (46.8000000000004, 1.5291842335973035e-10), (46.9000000000004, 1.1394560918694979e-10), (47.0000000000004, 7.6250089098287786e-11), (47.1000000000004, 3.9831863093744019e-11), (47.2000000000004, 4.6909311733187012e-12), (47.3000000000004, -2.9172706662988479e-11), (47.4000000000004, -6.17590504151769e-11), (47.5000000000004, -9.3068100083247079e-11), (47.6000000000004, -1.2309985566719886e-10), (47.7000000000004, -1.5185431716703212e-10), (47.8000000000004, -1.7933148458274711e-10), (47.9000000000004, -2.0553135791434367e-10), (48.0000000000004, -2.3045393716182192e-10), (48.1000000000004, -2.5409922232518167e-10), (48.2000000000004, -2.7646721340442307e-10), (48.3000000000004, -2.9755791039954597e-10), (48.4000000000004, -3.1737131331055058e-10), (48.5000000000004, -3.3590742213743679e-10), (48.6000000000004, -3.531662368802046e-10), (48.7000000000004, -3.6914775753885397e-10), (48.8000000000004, -3.8385198411338499e-10), (48.9000000000004, -3.9727891660379756e-10), (49.0000000000004, -4.0942855501009184e-10), (49.1000000000004, -4.2030089933226762e-10), (49.2000000000004, -4.2989594957032505e-10), (49.3000000000004, -4.3821370572426408e-10), (49.4000000000004, -4.4525416779408472e-10), (49.5000000000004, -4.5101733577978697e-10), (49.6000000000004, -4.5550320968137076e-10), (49.7000000000004, -4.5871178949883621e-10), (49.8000000000004, -4.6064307523218326e-10), (49.9000000000004, -4.6129706688141192e-10), (50.0000000000004, -4.6067376444652212e-10), (50.1000000000004, -4.5877316792751398e-10), (50.2000000000004, -4.5559527732438745e-10), (50.3000000000004, -4.5114009263714252e-10), (50.4000000000004, -4.4540761386577919e-10), (50.5000000000004, -4.3839784101029746e-10), (50.6000000000004, -4.3011077407069734e-10), (50.7000000000005, -4.2054641304697882e-10), (50.8000000000005, -4.097047579391419e-10), (50.9000000000005, -3.9758580874718659e-10), (51.0000000000005, -3.8418956547111288e-10), (51.1000000000005, -3.6951602811092077e-10), (51.2000000000005, -3.5356519666661027e-10), (51.3000000000005, -3.5167368309170039e-10), (51.4000000000005, -3.5956613190320658e-10), (51.5000000000005, -3.6709334018898752e-10), (51.6000000000005, -3.7425530794904316e-10), (51.7000000000005, -3.8105203518337354e-10), (51.8000000000005, -3.8748352189197853e-10), (51.9000000000005, -3.9354976807485832e-10), (52.0000000000005, -3.9925077373201275e-10), (52.1000000000005, -4.0458653886344194e-10), (52.2000000000005, -4.0955706346914587e-10), (52.3000000000005, -4.141623475491244e-10), (52.4000000000005, -4.1840239110337769e-10), (52.5000000000005, -4.2227719413190572e-10), (52.6000000000005, -4.257867566347084e-10), (52.7000000000005, -4.2893107861178578e-10), (52.8000000000005, -4.3171016006313791e-10), (52.9000000000005, -4.3412400098876469e-10), (53.0000000000005, -4.3617260138866622e-10), (53.1000000000005, -4.3785596126284244e-10), (53.2000000000005, -4.3917408061129342e-10), (53.3000000000005, -4.4012695943401905e-10), (53.4000000000005, -4.4071459773101943e-10), (53.5000000000005, -4.4093699550229445e-10), (53.6000000000005, -4.4079415274784422e-10), (53.7000000000005, -4.4028606946766865e-10), (53.8000000000005, -4.3941274566176787e-10), (53.9000000000005, -4.3817418133014174e-10), (54.0000000000005, -4.3657037647279031e-10), (54.1000000000005, -4.3460133108971363e-10), (54.2000000000005, -4.322670451809116e-10), (54.3000000000005, -4.2956751874638432e-10), (54.4000000000005, -4.2650275178613174e-10), (54.5000000000005, -4.2307274430015381e-10), (54.6000000000005, -4.1927749628845068e-10), (54.7000000000005, -4.1511700775102219e-10), (54.8000000000005, -4.1059127868786846e-10), (54.9000000000005, -4.0570030909898937e-10), (55.0000000000005, -4.0044409898438504e-10), (55.1000000000005, -3.948226483440554e-10), (55.2000000000005, -3.8883595717800046e-10), (55.3000000000005, -3.8248402548622023e-10), (55.4000000000005, -3.7576685326871469e-10), (55.5000000000005, -3.686844405254839e-10), (55.6000000000005, -3.6123678725652776e-10), (55.7000000000005, -3.5342389346184637e-10), (55.8000000000005, -3.4524575914143968e-10), (55.9000000000005, -3.3670238429530768e-10), (56.0000000000005, -3.2779376892345039e-10), (56.1000000000005, -3.185199130258678e-10), (56.2000000000005, -3.0888081660255995e-10), (56.3000000000005, -2.9887647965352676e-10), (56.4000000000005, -2.8850690217876831e-10), (56.5000000000005, -2.7777208417828457e-10), (56.6000000000005, -2.6667202565207552e-10), (56.7000000000005, -2.5520672660014117e-10), (56.8000000000005, -2.4337618702248152e-10), (56.9000000000005, -2.7149074069258483e-10), (57.0000000000005, -2.6786093141301644e-10), (57.1000000000005, -2.6423112213344806e-10), (57.2000000000005, -2.6060131285387967e-10), (57.3000000000005, -2.5697150357431123e-10), (57.4000000000005, -2.5334169429474289e-10), (57.5000000000005, -2.4971188501517445e-10), (57.6000000000005, -2.4608207573560606e-10), (57.7000000000005, -2.4245226645603768e-10), (57.8000000000006, -2.3882245717646929e-10), (57.9000000000006, -2.351926478969009e-10), (58.0000000000006, -2.3156283861733251e-10), (58.1000000000006, -2.279330293377641e-10), (58.2000000000006, -2.2430322005819574e-10), (58.3000000000006, -2.2067341077862732e-10), (58.4000000000006, -2.1704360149905894e-10), (58.5000000000006, -2.1341379221949055e-10), (58.6000000000006, -2.0978398293992216e-10), (58.7000000000006, -2.0615417366035375e-10), (58.8000000000006, -2.0252436438078538e-10), (58.9000000000006, -1.9889455510121697e-10), (59.0000000000006, -1.9526474582164858e-10), (59.1000000000006, -1.9163493654208019e-10), (59.2000000000006, -1.8800512726251181e-10), (59.3000000000006, -1.8437531798294342e-10), (59.4000000000006, -1.8074550870337503e-10), (59.5000000000006, -1.7711569942380664e-10), (59.6000000000006, -1.7348589014423825e-10), (59.7000000000006, -1.6985608086466984e-10), (59.8000000000006, -1.6622627158510145e-10), (59.9000000000006, -1.6259646230553307e-10), (60.0000000000006, -1.5896665302596465e-10), (60.1000000000006, -1.5533684374639626e-10), (60.2000000000006, -1.5170703446682788e-10), (60.3000000000006, -1.4807722518725949e-10), (60.4000000000006, -1.444474159076911e-10), (60.5000000000006, -1.4081760662812271e-10), (60.6000000000006, -1.3718779734855432e-10), (60.7000000000006, -1.3355798806898594e-10), (60.8000000000006, -1.2992817878941755e-10), (60.9000000000006, -1.2629836950984916e-10), (61.0000000000006, -1.2266856023028077e-10), (61.1000000000006, -1.1903875095071236e-10), (61.2000000000006, -1.1540894167114397e-10), (61.3000000000006, -1.1177913239157558e-10), (61.4000000000006, -1.081493231120072e-10), (61.5000000000006, -1.0451951383243881e-10), (61.6000000000006, -1.0088970455287041e-10), (61.7000000000006, -9.7259895273302018e-11), (61.8000000000006, -9.3630085993733631e-11), (61.9000000000006, -9.000027671416523e-11), (62.0000000000006, -8.6370467434596842e-11), (62.1000000000006, -8.2740658155028454e-11), (62.2000000000006, -7.9110848875460066e-11), (62.3000000000006, -7.5481039595891665e-11), (62.4000000000006, -7.2601104581422504e-11), (62.5000000000006, -7.2475215671473028e-11), (62.6000000000006, -7.2349326761523565e-11), (62.7000000000006, -7.2223437851574076e-11), (62.8000000000006, -7.20975489416246e-11), (62.9000000000006, -7.1971660031675124e-11), (63.0000000000006, -7.1845771121725648e-11), (63.1000000000006, -7.1719882211776172e-11), (63.2000000000006, -7.1593993301826696e-11), (63.3000000000006, -7.146810439187722e-11), (63.4000000000006, -7.1342215481927731e-11), (63.5000000000006, -7.1216326571978255e-11), (63.6000000000006, -7.1090437662028792e-11), (63.7000000000006, -7.0964548752079303e-11), (63.8000000000006, -7.0838659842129827e-11), (63.9000000000006, -7.0712770932180351e-11), (64.0000000000006, -7.0586882022230875e-11), (64.1000000000006, -7.0460993112281412e-11), (64.2000000000006, -7.0335104202331936e-11), (64.3000000000006, -7.020921529238246e-11), (64.4000000000006, -7.0083326382432997e-11), (64.5000000000006, -6.9957437472483534e-11), (64.6000000000006, -6.9831548562534058e-11), (64.7000000000006, -6.9705659652584595e-11), (64.8000000000006, -6.9579770742635119e-11), (64.9000000000006, -6.9453881832685656e-11), (65.0000000000006, -6.9327992922736193e-11), (65.1000000000006, -6.9202104012786717e-11), (65.2000000000006, -6.9076215102837254e-11), (65.3000000000006, -6.8950326192887778e-11), (65.4000000000006, -6.8824437282938315e-11), (65.5000000000006, -6.8698548372988839e-11), (65.6000000000005, -6.8572659463039376e-11), (65.7000000000005, -6.8446770553089912e-11), (65.8000000000005, -6.8320881643140436e-11), (65.9000000000005, -6.8194992733190973e-11), (66.0000000000005, -6.8069103823241497e-11), (66.1000000000005, -6.7943214913292034e-11), (66.2000000000005, -6.7817326003342571e-11), (66.3000000000005, -6.7691437093393095e-11), (66.4000000000005, -6.7565548183443619e-11), (66.5000000000005, -6.7439659273494156e-11), (66.6000000000005, -6.7313770363544693e-11), (66.7000000000005, -6.7187881453595217e-11), (66.8000000000005, -6.7061992543645754e-11), (66.9000000000005, -6.6936103633696278e-11), (67.0000000000005, -6.6810214723746815e-11), (67.1000000000005, -6.6684325813797352e-11), (67.2000000000005, -6.6558436903847876e-11), (67.3000000000005, -6.6432547993898413e-11), (67.4000000000004, -6.630665908394895e-11), (67.5000000000004, -6.6180770173999474e-11), (67.6000000000004, -6.6054881264049998e-11), (67.7000000000004, -6.5928992354100535e-11), (67.8000000000004, -6.5803103444151072e-11), (67.9000000000004, -6.5677214534201596e-11), (68.0000000000004, -6.5551325624252133e-11), (68.1000000000004, -6.5425436714302657e-11), (68.2000000000004, -6.5299547804353194e-11), (68.3000000000004, -6.5173658894403731e-11), (68.4000000000004, -6.5047769984454255e-11), (68.5000000000004, -6.4921881074504779e-11), (68.6000000000004, -6.4795992164555316e-11), (68.7000000000004, -6.4670103254605853e-11), (68.8000000000004, -6.4544214344656377e-11), (68.9000000000004, -6.4418325434706914e-11), (69.0000000000004, -6.4292436524757451e-11), (69.1000000000003, -6.4166547614807975e-11), (69.2000000000003, -6.4040658704858511e-11), (69.3000000000003, -6.3914769794909036e-11), (69.4000000000003, -6.3788880884959572e-11), (69.5000000000003, -6.3662991975010109e-11), (69.6000000000003, -6.3537103065060633e-11), (69.7000000000003, -6.3411214155111157e-11), (69.8000000000003, -6.3285325245161694e-11), (69.9000000000003, -6.3159436335212231e-11), (70.0000000000003, -6.3033547425262755e-11), (70.1000000000003, -6.2907658515313292e-11), (70.2000000000003, -6.2781769605363816e-11), (70.3000000000003, -6.2655880695414353e-11), (70.4000000000003, -6.252999178546489e-11), (70.5000000000003, -6.2404102875515414e-11), (70.6000000000003, -6.2278213965565938e-11), (70.7000000000003, -6.2152325055616475e-11), (70.8000000000003, -6.2026436145667012e-11), (70.9000000000002, -6.1900547235717536e-11), (71.0000000000002, -6.1774658325768073e-11), (71.1000000000002, -6.164876941581861e-11), (71.2000000000002, -6.1522880505869134e-11), (71.3000000000002, -6.1396991595919671e-11), (71.4000000000002, -6.1271102685970195e-11), (71.5000000000002, -6.1145213776020732e-11), (71.6000000000002, -6.1019324866071269e-11), (71.7000000000002, -6.0893435956121793e-11), (71.8000000000002, -6.0767547046172317e-11), (71.9000000000002, -6.0641658136222867e-11), (72.0000000000002, -6.0515769226273391e-11), (72.1000000000002, -6.0389880316323915e-11), (72.2000000000002, -6.0263991406374452e-11), (72.3000000000002, -6.0138102496424989e-11), (72.4000000000002, -6.0012213586475513e-11), (72.5000000000002, -5.988632467652605e-11), (72.6000000000002, -5.9760435766576574e-11), (72.7000000000001, -5.9634546856627111e-11), (72.8000000000001, -5.9508657946677635e-11), (72.9000000000001, -5.9382769036728171e-11), (73.0000000000001, -5.9256880126778708e-11), (73.1000000000001, -5.9130991216829232e-11), (73.2000000000001, -5.9005102306879756e-11), (73.3000000000001, -5.8879213396930306e-11), (73.4000000000001, -5.875332448698083e-11), (73.5000000000001, -5.8627435577031354e-11), (73.6000000000001, -5.8501546667081904e-11), (73.7000000000001, -5.8375657757132428e-11), (73.8000000000001, -5.8249768847182952e-11), (73.9000000000001, -5.8123879937233489e-11), (74.0000000000001, -5.799799102728402e-11), (74.1000000000001, -5.787210211733455e-11), (74.2000000000001, -5.7746213207385081e-11), (74.3000000000001, -5.7620324297435611e-11), (74.4000000000000, -5.7494435387486142e-11), (74.5000000000000, -5.7368546477536679e-11), (74.6000000000000, -5.7242657567587209e-11), (74.7000000000000, -5.7116768657637733e-11), (74.8000000000000, -5.699087974768827e-11), (74.9000000000000, -5.68649908377388e-11), (75.0000000000000, -5.6739101927789331e-11), (75.1000000000000, -5.6613213017839868e-11), (75.2000000000000, -5.6487324107890398e-11), (75.3000000000000, -5.6361435197940922e-11), (75.4000000000000, -5.6235546287991459e-11), (75.5000000000000, -5.610965737804199e-11), (75.6000000000000, -5.598376846809252e-11), (75.7000000000000, -5.5857879558143057e-11), (75.8000000000000, -5.5731990648193581e-11), (75.9000000000000, -5.5606101738244112e-11), (76.0000000000000, -5.5480212828294649e-11), (76.1000000000000, -5.5354323918345179e-11), (76.1999999999999, -5.522843500839571e-11), (76.2999999999999, -5.5102546098446247e-11), (76.3999999999999, -5.4976657188496771e-11), (76.4999999999999, -5.4850768278547301e-11), (76.5999999999999, -5.4724879368597838e-11), (76.6999999999999, -5.4598990458648368e-11), (76.7999999999999, -5.4473101548698899e-11), (76.8999999999999, -5.4347212638749429e-11), (76.9999999999999, -5.422132372879996e-11), (77.0999999999999, -5.409543481885049e-11), (77.1999999999999, -5.3969545908901027e-11), (77.2999999999999, -5.3843656998951558e-11), (77.3999999999999, -5.3717768089002082e-11), (77.4999999999999, -5.3591879179052619e-11), (77.5999999999999, -5.3465990269103149e-11), (77.6999999999999, -5.334010135915368e-11), (77.7999999999999, -5.3214212449204217e-11), (77.8999999999998, -5.3088323539254747e-11), (77.9999999999998, -5.2962434629305271e-11), (78.0999999999998, -5.2836545719355808e-11), (78.1999999999998, -5.2710656809406339e-11), (78.2999999999998, -5.2584767899456869e-11), (78.3999999999998, -5.2458878989507406e-11), (78.4999999999998, -5.233299007955793e-11), (78.5999999999998, -5.220710116960846e-11), (78.6999999999998, -5.2081212259658997e-11), (78.7999999999998, -5.1955323349709528e-11), (78.8999999999998, -5.1829434439760058e-11), (78.9999999999998, -5.1703545529810595e-11), (79.0999999999998, -5.1577656619861119e-11), (79.1999999999998, -5.145176770991165e-11), (79.2999999999998, -5.1325878799962187e-11), (79.3999999999998, -5.1199989890012717e-11), (79.4999999999998, -5.1074100980063241e-11), (79.5999999999998, -5.0948212070113778e-11), (79.6999999999997, -5.0822323160164309e-11), (79.7999999999997, -5.0696434250214839e-11), (79.8999999999997, -5.0570545340265376e-11), (79.9999999999997, -5.0444656430315907e-11), (80.0999999999997, -5.0318767520366431e-11), (80.1999999999997, -5.0192878610416967e-11), (80.2999999999997, -5.0066989700467498e-11), (80.3999999999997, -4.9941100790518028e-11), (80.4999999999997, -4.9815211880568565e-11), (80.5999999999997, -4.9689322970619089e-11), (80.6999999999997, -4.956343406066962e-11), (80.7999999999997, -4.9437545150720157e-11), (80.8999999999997, -4.9311656240770687e-11), (80.9999999999997, -4.9185767330821218e-11), (81.0999999999997, -4.9059878420871755e-11), (81.1999999999997, -4.8933989510922279e-11), (81.2999999999997, -4.8808100600972809e-11), (81.3999999999997, -4.8682211691023346e-11), (81.4999999999996, -4.8556322781073877e-11), (81.5999999999996, -4.8430433871124407e-11), (81.6999999999996, -4.8304544961174944e-11), (81.7999999999996, -4.8178656051225468e-11), (81.8999999999996, -4.8052767141275999e-11), (81.9999999999996, -4.7926878231326535e-11), (82.0999999999996, -4.7800989321377066e-11), (82.1999999999996, -4.767510041142759e-11), (82.2999999999996, -4.7549211501478127e-11), (82.3999999999996, -4.7423322591528657e-11), (82.4999999999996, -4.7297433681579188e-11), (82.5999999999996, -4.7171544771629725e-11), (82.6999999999996, -4.7045655861680255e-11), (82.7999999999996, -4.6919766951730779e-11), (82.8999999999996, -4.6793878041781316e-11), (82.9999999999996, -4.6667989131831847e-11), (83.0999999999996, -4.6542100221882377e-11), (83.1999999999995, -4.6416211311932914e-11), (83.2999999999995, -4.6290322401983438e-11), (83.3999999999995, -4.6164433492033969e-11), (83.4999999999995, -4.6038544582084506e-11), (83.5999999999995, -4.5912655672135036e-11), (83.6999999999995, -4.5786766762185566e-11), (83.7999999999995, -4.5660877852236103e-11), (83.8999999999995, -4.5534988942286627e-11), (83.9999999999995, -4.5409100032337158e-11), (84.0999999999995, -4.5283211122387695e-11), (84.1999999999995, -4.5157322212438225e-11), (84.2999999999995, -4.5031433302488756e-11), (84.3999999999995, -4.4905544392539286e-11), (84.4999999999995, -4.4779655482589817e-11), (84.5999999999995, -4.4653766572640347e-11), (84.6999999999995, -4.4527877662690884e-11), (84.7999999999995, -4.4401988752741415e-11), (84.8999999999995, -4.4276099842791939e-11), (84.9999999999994, -4.4150210932842476e-11), (85.0999999999994, -4.4024322022893006e-11), (85.1999999999994, -4.3898433112943537e-11), (85.2999999999994, -4.3772544202994074e-11), (85.3999999999994, -4.3646655293044604e-11), (85.4999999999994, -4.3520766383095128e-11), (85.5999999999994, -4.3394877473145665e-11), (85.6999999999994, -4.3268988563196195e-11), (85.7999999999994, -4.3143099653246732e-11), (85.8999999999994, -4.3017210743297263e-11), (85.9999999999994, -4.2891321833347787e-11), (86.0999999999994, -4.2765432923398324e-11), (86.1999999999994, -4.2639544013448854e-11), (86.2999999999994, -4.2513655103499385e-11), (86.3999999999994, -4.2387766193549922e-11), (86.4999999999994, -4.2261877283600452e-11), (86.5999999999994, -4.2135988373650976e-11), (86.6999999999993, -4.2010099463701513e-11), (86.7999999999993, -4.1884210553752044e-11), (86.8999999999993, -4.1758321643802574e-11), (86.9999999999993, -4.1632432733853111e-11), (87.0999999999993, -4.1506543823903635e-11), (87.1999999999993, -4.1380654913954166e-11), (87.2999999999993, -4.1254766004004702e-11), (87.3999999999993, -4.1128877094055233e-11), (87.4999999999993, -4.1002988184105763e-11), (87.5999999999993, -4.08770992741563e-11), (87.6999999999993, -4.0751210364206824e-11), (87.7999999999993, -4.0625321454257355e-11), (87.8999999999993, -4.0499432544307892e-11), (87.9999999999993, -4.0373543634358422e-11), (88.0999999999993, -4.0247654724408953e-11), (88.1999999999993, -4.0121765814459483e-11), (88.2999999999993, -3.9995876904510014e-11), (88.3999999999993, -3.9869987994560544e-11), (88.4999999999992, -3.9744099084611081e-11), (88.5999999999992, -3.9618210174661612e-11), (88.6999999999992, -3.9492321264712136e-11), (88.7999999999992, -3.9366432354762673e-11), (88.8999999999992, -3.9240543444813203e-11), (88.9999999999992, -3.9114654534863734e-11), (89.0999999999992, -3.898876562491427e-11), (89.1999999999992, -3.8862876714964801e-11), (89.2999999999992, -3.8736987805015325e-11), (89.3999999999992, -3.8611098895065862e-11), (89.4999999999992, -3.8485209985116392e-11), (89.5999999999992, -3.8359321075166923e-11), (89.6999999999992, -3.823343216521746e-11), (89.7999999999992, -3.8107543255267984e-11), (89.8999999999992, -3.7981654345318514e-11), (89.9999999999992, -3.7855765435369051e-11), (90.0999999999992, -3.7729876525419582e-11), (90.1999999999992, -3.7603987615470112e-11), (90.2999999999991, -3.7478098705520643e-11), (90.3999999999991, -3.7352209795571173e-11), (90.4999999999991, -3.722632088562171e-11), (90.5999999999991, -3.7100431975672234e-11), (90.6999999999991, -3.6974543065722771e-11), (90.7999999999991, -3.6848654155773302e-11), (90.8999999999991, -3.6722765245823832e-11), (90.9999999[...]

list_plot(zip(t,sol[:,0]))
list_plot(zip(t,sol[:,1]))

#set up
var('R', 'J')
system = [4*R + J, -J + R] # R', J'
ic = (1,1)
t = srange(0, 1, .1)

(R, J)

# solve

sol = desolve_odeint(system, dvars=[R,J], ics=ic, times=t)

# view output

#trajectory
list_plot(sol, axes_labels=['R','J'])

[(0.000000000000000, 1.0), (0.100000000000000, 1.6157792168707819), (0.200000000000000, 2.5416026936833882), (0.300000000000000, 3.9401515644184388), (0.400000000000000, 6.0587020309759314), (0.500000000000000, 9.2731999276150034), (0.600000000000000, 14.155290102783971), (0.700000000000000, 21.574254513645933), (0.800000000000000, 32.852042082199389), (0.900000000000000, 49.999042128846817)]

# time series
# zip(t,sol[:,0])
list_plot(zip(t,sol[:,0])) + list_plot(zip(t,sol[:,1]), color="red")

# plot_vector_field

plot_vector_field(DEs, (R,-3,3), (J, -3,3)) + list_plot(sol) + point(ic, color="red", size=40)