Chapter 3, Problem 3.8E

For the integro-differential equation,
$\begin{array}{l}\frac{d^{2}x}{d{t}^2}+4\frac{dx}{dt}+3x=\stackrel{\stackrel{t}{f}}{20}{e}^{-\tau }d\tau \\ \text{with}\frac{dx}{dt}\left(0\right)=x\left(0\right)=0.\end{array}$
a. Find $x\left(t\right)$
b. What is the limiting value of t and $t\to \infty$ ?