Solve the following initial value problem using Laplace transform:

(a)

\[\frac{d y}{d t}=-y+e^{-3 t}, \quad y(0)=2\]

(b)

\[\frac{d y}{d t}+11 y=3, \quad y(0)=-2\]

(c)

\[\frac{d y}{d t}+2 y=2 e^{7 t}, \quad y(0)=0\]