Nonseparable ODE which method to use

[Dustinsfl]

Homework Statement

$$
\left(\frac{du}{dx}\right)^2 = au^2 + bu + c
$$

Homework Equations

The Attempt at a Solution

What method is used to solve and ODE of this form

 

[hilbert2]

Isn't that equivalent to $\frac{du}{\sqrt{au^{2}+bu+c}}=\pm dx$ ? Seems to be separable after all.