Question

Differential equation question

Answer 1

It's not a Cauchy-Euler equation so I can't use the guess y(t)=t^r . I'm not given a solution so I can't use reduction of order.

I tried making a change of variables by letting w=y' but that doesn't help the fact I have a y.

My only other option, (which I haven't tried) is to use the hint given in the question and find y' and y" and substitute. That might simplify down to a equation in which I can solve for the characteristic equation so I can find a particular solution.

Is that correct or is there there something i'm not noticing?

Answer 2

I actually tried a change of variables but that doesn't help either.