Chapter 1.3, Problem 31P

In Problems $27$ through $31$, verify that $y\left(t\right)$ satisfies the given differential equation. Then determine a value of the constant $C$ so that $y\left(t\right)$ satisfies the given initial condition.

$2y\text{'}+ty=2;y\left(t\right)=e^{-t^2/4}{\displaystyle {\int }_0^t{e}^{s^2/4}}ds+C{e}^{-t^2/4},y\left(0\right)=1$