Picard Iteration, with a 2nd order ODE

[][nstigator]

Homework Statement

Ive been told to perform 2-3 Picard Iterations on the following problem

Homework Equations

y'' = 6y^2

With initial conditions:

y(0) = 0
y'(0)= -2

The Attempt at a Solution

In class we've gone through how to perform picard iterations and it has been easy so far... however this is the first time it has had a second order term at the front. Through internet searches and reading our given notes, I am still not sure how to treat this so I can't really start to try and solve it...

Would anyone be able to give me a nudge in the right direction?Thanks in advance

 

[Leptos]

It's just substitution, i.e f(y, y', y'')-> f(y, p, pdp/dy).
You assume there exists a p: p = y', pdp/dy = y'' and at the end you back substitute for y. This transforms a second order ODE into a first order ODE.