Solving ODE with Bernoulli's Method: y''+(y')2 = y

[manenbu]

Homework Statement

y''+(y')² = y, y(0)=1, y'(0)=1/√2

Homework Equations

Bernoulli's method.

The Attempt at a Solution

Using the substitution p=y' I get this:
p'p + p² = y, so I can use z=p² to solve this.
However, I'm getting something wrong.
I think it could be because I'm having too much letters - p, z, y, x so I might be missing some chain rules.

 

[andrew.c]

Not worked through this, but using the substitution p = y', surely you would get:

p'+p^2 = y and NOT p'p +p^2?

 

[manenbu]

but I'm using p(y), not p(x)
so y'' = dp/dy dy/dx = dp/dy p = p' p

 

[manenbu]

oh well, I got it. Took me 2 pages of text. If you're interested I can post the solution here. :)