Freier_Fall.sagews

# freier Fall mit Luftwiderstand
x = var('x'); y = function('y')
DE = diff(y(x), x) == -0.2/2*y(x) + 10
s=desolve(DE, [y(x),x])
show(s)
sol = []
for i in srange(0, 160, 20):
 sol.append(desolve(DE, [y(x), x], ics=[1, i]))
 sol.append(desolve(DE, [y(x), x], ics=[-1, i]))
g = plot(sol, x, 0,100,color='red')
y = var('y')
R_S=-0.2/2*y + 10
g +=plot_slope_field(R_S,(x,0,100),(y,0,150),color='blue',gridlines=True,  axes_labels=['Zeit $t$','Fallgeschwindigkeit $v(t)$'])
#g += plot_vector_field((x, 2*y+x^3), (x,-2,2), (y,-1,1))
g.show(ymin=0, ymax=150)

$\displaystyle {\left(C + 100 \, e^{\left(\frac{1}{10} \, x\right)}\right)} e^{\left(-\frac{1}{10} \, x\right)}$