Nonlinear differential equation

[CINA]

Homework Statement

$$y''+4\left(y'\right)^{2}+8=0$$

Homework Equations

$$u=y'?$$

The Attempt at a Solution

I don't really know where to start, do I use u=y' substituted? So, y''=u*(du/dy)?

That leads to $$u\frac{du}{dy}+4u^{2}+8=0$$

I don't think this is correct, since it leads to $$y(x)=-\frac{u^{2}}{16}-\frac{ln (u)}{4}$$

 

[jackmell]

Why not just let u=y' and get:

$$u'+4u^2+8=0$$

and try and remember that whenever you have a first-order equation with a $u^n$ term, try to see if it's a Bernoulli equation which is easily solved.