Differential equation with $(\frac{dx}{dt})^2$ I have had very little training in differential equations, so this might be a stupid question. Is it okay to solve something like $t = x^2({dx\over dt} )^2$, by doing: $t(dt)^2=t^2(dx)^2 \rightarrow {t^2\over2}dt={x^3\over3}dx$ and then integrating again? 

Hint: It should be: $\dfrac{dx}{dt} = \pm \dfrac{\sqrt{t}}{x} \to xdx = \pm \sqrt{t}dt$
