DE

Requesting knowledge of how to solve non linear differential equations. GO!

There's no standard way.

Try a series solution, maybe there's a clever substitution, if it's a physical system and you can see a trivial solution, that should be the only one by determinism I think.

d²x/dt² = (dx/dt)^2  x = ?

a = d²x/dt²
v = dx/dt

a = v²
dv/dt = v²
dv/v² = dt
-1/v = t + c
v = -1/(t+c)
x = -ln(t+c) + k

>>3
kill yourself