Power Series Recurrence Relation Problem

[jegues]

Homework Statement

See figure attached, we are asked to use power series to solve the differential equation.

Homework Equations

The Attempt at a Solution

I'm confused as to how to deal with the -1 in the indices of one of my summations.

I could add the term on the outside and still simplify the two summations but how do I get past this point?

Can I just let a2 = 0?

Thanks again!

 

[vela]

Looks okay so far. Every term in the series has to be equal to 0, from which it follows that a₂=0, or, if you prefer, you can solve for a₂ by letting x=0.