Differential equation (to solve analytically)

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Homework Help Overview

The discussion revolves around solving a differential equation analytically, specifically of the form (x^2+1)y' = x^2+x-1+4xy. The original poster expresses uncertainty about how to approach the problem and considers the possibility of using a series solution.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss rewriting the equation in a linear form and suggest using an integrating factor. There is also a clarification regarding the correct form of the integrating factor, indicating some confusion about the signs in the expressions.

Discussion Status

The discussion is ongoing, with participants providing guidance on how to manipulate the equation and clarify the integrating factor. There is acknowledgment of a potential error in the sign, which indicates active engagement with the problem.

Contextual Notes

The original poster indicates a lack of familiarity with the topic, which may affect their understanding of the proposed methods. The conversation reflects a collaborative effort to clarify the steps involved in solving the equation.

dragonblood
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(x^2+1)y'=x^2+x-1+4xy
How can I solve this equation analytically?
I have almost no idea. I thought that y might be a series...please help :)

Homework Statement


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The Attempt at a Solution

 
Last edited:
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If you write that as [itex](x^2+ 1)dy/dx- 4xy= x^2+ x- 1[/itex] or
[tex]\frac{dy}{dx}- \frac{4x}{x^2+ 1}y= \frac{x^2+ x- 1}{x^2+ 1}[/itex]<br /> a linear differential equation. Then <br /> [tex]e^{\int {4x}{x^2+1} dx}[/tex] is an integrating factor. Multiplying the entire equation by it will make the left side an "exact" derivative.[/tex]
 
Let me just clarify that integrating factor for you ivy =] [tex]e^{- \int \frac{4x}{x^2+1} dx}[/tex]
 
Allright :) Thanks peeps!
 
Dang! Dropped a sign, didn't I?
 

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