Chapter 1.3, Problem 28P

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.

$y\text{'}+\left(\sin t\right)y=0;y\left(t\right)=C{e}^{\cos t},y\left(\pi \right)=1$