Verify that $y_1(t) = t^2$ and $y_2(t) = t^{-1}$ are two solutions of the differential equation $t^2y^{''}-2y = 0$ for $t>0$. Then show that $c_1t^2 +c_2t^{-1}$ is also a solution of this equation for any $c_1$ and $c_2$.
For the first part, I know it is a solution since if I plug in $y_1(t) = t^2$ and $y_2(t) = t^{-1}$ into the differential equation it will give me $0$ which is the solution to the differential equation, but how can I do the second part. Showing that $c_1t^2 +c_2t^{-1}$ is a solution? If I plug those in the differential equation I get something that isn't equal to zero.