- #1

TheFerruccio

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## Homework Statement

Find a basis of solutions.

## Homework Equations

[tex](1-x^2)y''+(1-x)y'-3y = 0[/tex]

## The Attempt at a Solution

Using the series approach, having:

[tex]y=\sum_{n=0}^{\infty}a_nx^n[/tex]

I ended up with an equation representing the coefficients for [tex]x^0[/tex]

[tex]2a_2+a_1-3a_0 = 0[/tex]

I'm confused because this is the first time I have encountered three coefficients for the same power of x. I just want to verify that I didn't make an algebra mistake, because I am used to finding that certain coefficients are linked to even powers, while others are linked to odd powers.