Chapter 4.5, Problem 2E

Given that $y_1\left(t\right)=\left(1/4\right)\sin 2t$ is a solution to $y^{\prime \prime }+2y^{\prime }+4y=\cos 2t$ and that $y_2\left(t\right)=\raisebox{1ex}{$t$}\!\left/ \!\raisebox{-1ex}{$4$}\right.-\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$8$}\right.$ is a solution to $y^{\prime \prime }+2y^{\prime }+4y=t,$ use the superposition principle to find the solutions to the following:

a. $y^{\prime \prime }+2y^{\prime }+4y=t+\cos 2t$ .

b. $y^{\prime \prime }+2y^{\prime }+4y=2t-3\cos 2t$ .

c. $y^{\prime \prime }+2y^{\prime }+4y=11t-12\cos 2t$ .