solving nonlinear second order ordinary differential equations numerically

edit

Thanks Eric,

I meant the g(t) term to be a y(t) term so the equation looks like

y''(t)+f(t)(y'(t))^2 +y(t)=0

I don't think this is easily turned into a first order equation.

Wayne

@eric_g's solution can handle this. Just replace $g(t)$ with $y(t)$. Here is an example with $f(t)=-2+\frac{t}{1+t}$.

var('t y z')
P=desolve_system_rk4([z,-z^2*(-2+t/(1+t))-y],[y,z],ics=[0.1,10,2],ivar=t,end_points=100)
Q=[ [t1,y1] for t1,y1,z1 in P]
line(Q).show()

Thanks very much Calc314! Clearly I have a lot to learn. I will work on this.