Chapter 9.3, Problem 43E

a.

To determine

The solution of the linear differential equation $\frac{d^{2}x}{d{t}^2}+5\frac{dx}{dt}+6x=\cos \left(t\right)$ .

b.

To determine

The long term behavior of the solution $x(t)=A{e}^{-2t}+B{e}^{-3t}+\frac{1}{10}\left(\cos t+\sin t\right)$ of the linear differential equation $\frac{d^{2}x}{d{t}^2}+5\frac{dx}{dt}+6x=\cos \left(t\right)$ .