Q1: Solve the following IVPs by using the table of Laplace Transform.\\
a) $y' - y = te^t \sin t$, $y(0) = 0$\
b) $ty'' + (t - 3)y' + y = 0$, $y(0) = 0$, $y'(0) = 0$\
c) $y'' + 16y = f(t)$, $y(0) = 0$, $y'(0) = 1$, where\\$f(t) = \begin{cases} \cos 4t, & 0 \le t < \pi\\0, & t \ge \pi \end{cases}$