Differential equation (to solve analytically)

[dragonblood]

(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

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

If you write that as $(x^2+ 1)dy/dx- 4xy= x^2+ x- 1$ 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 /> $$e^{\int {4x}{x^2+1} dx}$$ is an integrating factor. Multiplying the entire equation by it will make the left side an "exact" derivative.[/tex]

 

[djeitnstine]

Let me just clarify that integrating factor for you ivy =] $$e^{- \int \frac{4x}{x^2+1} dx}$$

 

[dragonblood]

Allright :) Thanks peeps!

 

[HallsofIvy]

Dang! Dropped a sign, didn't I?