Verify that $y_1(t)=t^2$ and $y_2(t)=t^{-1}$ are two solutions of the differential equation

$t^2{y}^{\text{'}\text{'}}-2y=0,$ for $t>0$

Then show that $y=c_1{t}^2+c_2{t}^{-1}$ is also a solution of this equation for any $c_1$ and $c_2.$