Originally Posted by
Prove It Yes it's right.
So multiply both sides by the integrating factor to get
$\displaystyle \displaystyle t^{-2}\frac{dy}{dt} - 2t^{-3}\,y = 3t^{-4}$
$\displaystyle \displaystyle \frac{d}{dt}(t^{-2}y) = 3t^{-4}$.
You should be able to go from here.