Have to find three ways of solving (only have one successful)

[Mabbott608]

Homework Statement

x*y'' - y' = 3x^2

The Attempt at a Solution

so far i have used cauch-euler and solved it. i was trying to use linear de and power series to solve, but with little success. Am i on the right track? If not, which method should i be using to find the solution?

 

[Mark44]

Homework Statement

x*y'' - y' = 3x^2

The Attempt at a Solution

so far i have used cauch-euler and solved it. i was trying to use linear de and power series to solve, but with little success. Am i on the right track? If not, which method should i be using to find the solution?

I don't recall the Cauchy-Euler method is, so if that worked for you, great. Power series should work, so if you're having problems, show us what you've done.

You can also make the substitutiion u = y', u' = y'' to make the equation first order, and find an integrating factor. Once you have found u, integrate to get y.