I have been confused by this differential equation for several days. I have an equation like this:
Where m,c,n are known parameters. And V(y(t)) is a two dimensional coordinate data set $(y(t1),V1),(y(t2),V2),...,(y(ti),Vi)$ and I don't know the exact analytical expression of $V(t)$. So, is it possible to solve this differential equation? By what kind of method or algorithm?
I know maybe I could solve this equation by fitting the data set $V(y(t))$, and obtain an analytical expression, then substitute it into the equation and solve it. But that maybe inaccurate and sometimes it is difficult to fit the curve. So is it possible to solve this kind of equation that contains a term without analytical expression in other methods?
For example, let m=1, c=0.05, n=0.01, and let $V'(y(t))$:
How to solve this equation use Mathematica?