Chapter 10.7, Problem 33P

For Problems 27-41, solve the given initial-value problem.

$y^{\prime }-3y=10e^{-\left(t-a\right)}\sin \left[2\left(t-a\right)\right]u_a\left(t\right)$, $y\left(0\right)=5$, where $a$ is a positive constant.