- #1

dp182

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- 0

## Homework Statement

consider the initial value problem (1-x)y

^{,,}+xy

^{,}-2y=0 find the series solution up to the term with x

^{6}

## Homework Equations

(1-x)y

^{,,}+xy

^{,}-2y=0

## The Attempt at a Solution

assuming the answer has the form [itex]\Sigma[/itex]a

_{n}x

^{n}

that gives y

^{,,}=[itex]\Sigma[/itex]na

_{n}x

^{n-1}and y

^{,,}=[itex]\Sigma[/itex]n(n-1)a

_{n}x

^{n-2}then plugging these back in and getting rid of the x

^{n-2}and x

^{n-1}you get the equation [itex]\Sigma[/itex](n+2)(n+1)a

_{n+2}x

^{n}-[itex]\Sigma[/itex]n(n+1)a

_{n+1}x

^{n}+[itex]\Sigma[/itex]na

_{n}x

^{n}-2[itex]\Sigma[/itex]a

_{n}x

^{n}so what I'm wondering is how do you replace the a

_{n+1}with an a

_{n}so you can solve for a

_{n+2}