Find the complete time-domain solutions for the following differential equations using Laplace transforms:
(a) \frac{d^{3} x}{d t^{3}}+4 x=e^{t} \text { with } x(0)=0, \quad \frac{d x(0)}{d t}=0, \quad \frac{d^{2} x(0)}{d t^{2}}=0
(b) \frac{d x}{d t}-12 x=\sin 3 t \quad x(0)=0
(c) \frac{d^{2} x}{d t^{2}}+6 \frac{d x}{d t}+25 x=e^{-t} \quad x(0)=0, \quad \frac{d x(0)}{d t}=0