# 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 :)
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Last edited:

#### HallsofIvy

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

#### djeitnstine

Gold Member
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?

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