Solution to an ODE using Power Series Method

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Homework Help Overview

The discussion revolves around solving a non-homogeneous ordinary differential equation (ODE) using the power series method. The original poster expresses difficulty in applying this method, particularly with the presence of x-variables not directly associated with y.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore the possibility of transforming the ODE into a standard form suitable for integrating factors. There is a suggestion to divide by x to facilitate this transformation. However, the original poster emphasizes the requirement to use the power series method, raising questions about how to proceed with this specific approach.

Discussion Status

The discussion is ongoing, with participants offering different perspectives on how to approach the problem. Some guidance has been provided regarding integrating factors, but the original poster is focused on adhering to the power series method, indicating a lack of consensus on the preferred method of solution.

Contextual Notes

The original poster notes that the assignment explicitly requires the use of the power series method, which adds a constraint to the discussion. There is also uncertainty regarding how to handle the x-variables in the context of this method.

eden2291
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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.
 
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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 said:
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.
 
First step, write y as a power series...
 

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