Chapter 5.3, Problem 1E

In Problems 1-7, convert the given initial value problem into an initial value problem for a system in normal form.

$y^{\prime \prime }\left(t\right)+t{y}^{\prime }\left(t\right)-3y\left(t\right)=t^2$;

$y\left(0\right)=3$, $y^{\prime }\left(0\right)=-6$