I'm having some trouble solving a simple differential equation, and yes I'm a bit lazy to check my notes.

It's a simple one, here it is : We have that $\displaystyle x'=f(t,x)$, $\displaystyle x(0)=0$. Use the fact that $\displaystyle dt/dx=(dx/dt)^{-1}$ when dx/dt≠0.

$\displaystyle f(t,x)=x^{-2}$.

It's certainly a beginner question but I have a doubt in this case : x'=dx/dt? I guess yes, since otherwise I don't see what could be x'!