Question

Solve the differential equation

Answer 1

\[2t^2y''+4ty'-2y=0\]

Given , t<0

Answer 2

I know this is a cauchy-Euler equation and my guess is y(t)=(-t)^r but i'm not sure where to go from there.

Answer 3

So \[y(t) = (-t)^r\]

\[y'(t)=r(-t)^{(r-1)}\]

\[y''(t)=r(r-1)(-t)^{r-2}\]

Answer 4

Substituting:

\[2t^2(r(r-1)(-t)^{r-2})+4t(r(-r)^{r-1})-2(-t)^r=0\]

Answer 5

How do I continue? >.< .

Answer 6

Nvm, got it.