Problem $4.$ Consider the ODE and IC:

$x^{}+3x=e^{-t},$

$x(0)=2.$

a$)$ Use the trial solution and variation of constants

methods to determine the solution $x(t)$ analytically.

b$)$ Use Matlab to plot the analytical solution $x(t)$

over the interval tin$[0,2].$

c$)$ Calculate the solution numerically in Matlab, plot

it$,$ and compare it to the analytical solution.

d$)$ Include your Matlab codes in your submission.