I came across a second order non-linear DE. The equation is $m\ddot x$+$(c\dot x)^2$+$kx$=g.
I have no idea where to start to solve this DE, can this even be solved analytically or if I have to approximate it with numerical methods. If so what methods do I have to use?
I tried to solve it for a half-hour and could only rearrange the equation and try a substitution which didn't help. Any help is appreciated
Best Answer
One can express $t$ as a function of $x$, function defined by an integral (no simpler closed form).
There is no closed form for the inverse function $x(t)$.
On practical viewpoint, better use a numerical method for solving.