Differential equation (to solve analytically)

(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

Science Advisor
41,626
821
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]
a linear differential equation. Then
[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.
 

djeitnstine

Gold Member
614
0
Let me just clarify that integrating factor for you ivy =] [tex]e^{- \int \frac{4x}{x^2+1} dx}[/tex]
 
Allright :) Thanks peeps!
 

HallsofIvy

Science Advisor
41,626
821
Dang! Dropped a sign, didn't I?
 

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