Chapter 4.5, Problem 1E

Given that $y_1\left(t\right)=\cos t$ is a solution to

$y^{\prime \prime }-y^{\prime }+y=\sin t$

and $y_2\left(t\right)=e^{2t}/3$ is a solution to

$y^{\prime \prime }-y^{\prime }+y=e^{2t}$,

use the superposition principle to find solutions to the following differential equations:

a. $y^{\prime \prime }-y^{\prime }+y=5\sin t$.

b. $y^{\prime \prime }-y^{\prime }+y=\sin t-3e^{-t}$.

c. $y^{\prime \prime }-y^{\prime }+y=4\sin t+18e^{2t}$.