Chapter 3, Problem 3.10E

Which solutions of the following equations will exhibit convergent behavior? Which are oscillatory?
Assume zero initial conditions for y and its derivatives
a. $\frac{d^{3}x}{d{t}^3}+2\frac{d^{2}x}{d{t}^2}+2\frac{dx}{dt}+x=3$
b. $\frac{d^{2}x}{d{t}^2}-x=2e^t$
c. $\frac{d^{3}x}{d{t}^3}+x=\sin t$
d. $\frac{d^{2}x}{d{t}^2}+\frac{dx}{dt}=4$
Note: All of the above differential equations have one common factor in their characteristic equations.