a$.$ Show that the solution $(7)$ of the general linear equation $(1)$ can be written in the form

$y=c{y}_1(t)+y_2(t)$

where $c$ is an arbitrary constant.

b$.$ Show that $y_1$ is a solution of the differential equation

$y^{\text{'}}+p(t)y=0$

corresponding to $g(t)=0.$

c$.$ Show that $y_2$ is a solution of the full linear equation $(1).$ We see later $($for example, in Section $3\mathrm{.}5)$ that solutions of higherorder linear equations have a pattern similar to equation $(29).$