Chapter 4.7, Problem 30E

To determine

To show:

$k_1{y}_1+k_2{y}_2$ is a solution on $I$ to the equation

$y^{″}\left(t\right)+p\left(t\right)y^{\prime }\left(t\right)+q\left(t\right)y\left(t\right)=k_1{g}_1\left(t\right)+k_2{g}_2\left(t\right)$.