- #1

TheFerruccio

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## Homework Statement

Use method of Frobenius to solve this equation:

##y''(x)-y'(x)=x##

## Homework Equations

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## The Attempt at a Solution

Seek an answer of the form

##y=\sum _{n=0}^{\infty } a_n x^{n+r}##

Plug into the equation to get...

##\sum _{n=0}^{\infty } a_{n+1} (n+r) (n+r-1) x^{n+r-2}-\sum _{n=0}^{\infty } a_n

(n+r) x^{n+r-1}=x##

Now, for every previous attempt I have had at Frobenius method, I am used to having a homogeneous equation. I'm likely having a brain fart because I do not see how I would put this equation into a homogeneous form so I can get the correct indicial equation and solve for my roots. Does anyone have a suggestion for the next proper step to take?