2039.sagews

a=3
b=4
c=5
d=-2
t=var('t')
x=function('x',t)
y=function('y',t)
DE1=diff(x,t)-a*x- b*y==0
DE2=diff(y,t)-c*x-d*y==0
sol=desolve_system((DE1,DE2),[x,y],[0,1,-1])
show(sol)
solnx, solny = sol[0].rhs(), sol[1].rhs()
plot([solnx, solny], (0,1), color='red'), parametric_plot([solnx, solny], (0,1), color='red')

\newcommand{\Bold}[1]{\mathbf{#1}}\left[x\left(t\right) = -\frac{1}{35} \, {\left(\sqrt{105} \sinh\left(\frac{1}{2} \, \sqrt{105} t\right) - 35 \, \cosh\left(\frac{1}{2} \, \sqrt{105} t\right)\right)} e^{\left(\frac{1}{2} \, t\right)}, y\left(t\right) = \frac{1}{7} \, {\left(\sqrt{105} \sinh\left(\frac{1}{2} \, \sqrt{105} t\right) - 7 \, \cosh\left(\frac{1}{2} \, \sqrt{105} t\right)\right)} e^{\left(\frac{1}{2} \, t\right)}\right]

(, )

a=4
b=-3
c=2
t=var('t')
x=var('x')
y=function('y',x)
DE1=diff(y,x,2)+a*diff(y,x) + b*y - c*sin(c*x)==0
sol=desolve(DE1,[y,x],[0,0,2])
show(sol)
plot3d(sol,(-10,10),(-10,10),color='red')

\newcommand{\Bold}[1]{\mathbf{#1}}-\frac{1}{791} \, {\left(143 \, \sqrt{7} - 56\right)} e^{\left(-{\left(\sqrt{7} + 2\right)} x\right)} + \frac{1}{791} \, {\left(143 \, \sqrt{7} + 56\right)} e^{\left({\left(\sqrt{7} - 2\right)} x\right)} - \frac{14}{113} \, \sin\left(2 \, x\right) - \frac{16}{113} \, \cos\left(2 \, x\right)