Differential equations using Series

[stosw]

Homework Statement

Given that y₁(t) = t is a solution of t²y'' + ty' - y= 0 find all solutions.

The Attempt at a Solution

I already put it into mathbin asking somewhere else for help and it doesn't look like i can copy paste that syntax to here.

http://mathbin.net/56336

Could someone tell me if that is correct so far?
If so can you tell me where to go from there?
If not could you tell me where I made a mistake?

thank you.

 

[stosw]

After many hours of getting no where, I realized that the correct method to solve this problem is Reduction of order.

The answer is y₂(t) = 1/t.