Solution to an ODE using Power Series Method

[eden2291]

Homework Statement

xy'-(x+2)y=-2x²-2x

Homework Equations

The Attempt at a Solution

I'm clueless as to how to solve this as I'm only experienced in using the power series method with homogenous ODE's. Even if I make this homogenous, I don't know what to do with the x-variables that are not attached to some y-variable.

Thanks you so much for any help.

 

[Char. Limit]

I recommend dividing both sides of the equation by x, whereupon you will then get an equation in this form:

$$\frac{dy}{dx} + p(x) y = q(x)$$

Which you can then solve using an integrating factor.

 

[dextercioby]

Do you know what the power series method means ? (The ODE can be integrated directly using an integrating factor http://en.wikipedia.org/wiki/Integrating_factor).

 

[eden2291]

Do you know what the power series method means ? (The ODE can be integrated directly using an integrating factor http://en.wikipedia.org/wiki/Integrating_factor).

I do. And I know it can be solved using an integrating factor, but the directions for the assignment explicitly state that the solution must be obtained using the power series method.

 

[hunt_mat]

First step, write y as a power series...