Problem solving ODE Doing my homework on analytical mechanics I stucked on the equation of the next form: $$\left(\frac{dy}{dt}\right)^2=f(y)$$ I need to find dependence of $y$ on $t$. I had an idea to differentiate it to make it linear relative to $\frac{dy}{dt}$ term. But on the RHS there is a nasty function which will become much bigger, moreover I will need additional initial condition. Maybe you could show me some other more convenient method? I know this should be something simple but I slept bad tonight and I just need your directions.

You can just take the square root and you will have two answers after separating the variables and integrating. 
$$\frac{dy}{dt}=\pm\sqrt{f(y)}\iff \frac{dy}{\pm\sqrt{f(y)}}=dt\iff\int \frac{dy}{\pm\sqrt{f(y)}}=\int dt$$
Solution 1: $$\boxed{\int\frac{dy}{\sqrt{f(y)}}=t+c}$$
Solution 2: $$\boxed{\int\frac{dy}{\sqrt{f(y)}}=-t+c}$$
I don't think you can do any better without knowing more about $f(y)$.
