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.