Chapter 3, Problem 3.12E

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