Chapter 1.3, Problem 29P

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.

$y\text{'}+\left(2/t\right)y=\left(\cos t\right)/t^2;y\left(t\right)=\left(\sin t\right)/t^2+C/t^2,y\left(1\right)=\frac{1}{2}$