Finding the general solution to y'' - 2(y')² = 0

[scarlets99]

Homework Statement

What is the general solution to y'' - 2(y')^2 = 0 ?

Homework Equations

The Attempt at a Solution

Let u = y '

u ' - 2u^2 = 0
u ' = 2u^2
u = (2 / 3)u^3 + C

This cannot be solved using separation of variables, what is done?

 

[thebigstar25]

your first step is correct when you chose u=y' , then you got the equation:
u'-2u^2=0 ,then : u'=2u^2

I believe that the last step you did is not correct, as far as i remember you should write u' = du/dx (or du/dt) according to what function is y originally, then from there you can use separation of variables .. :)