$(1)$ Suppose that the function $y_1(t)$ is a solution of

$y^{\text{'}\text{'}}+a_1{y}^{\text{'}}+a_{0}y=cos(4t)$

$(2)$ Also suppose that the function $y_2(t)$ is a solution of

$y^{\text{'}\text{'}}+a_1{y}^{\text{'}}+a_{0}y=0$

Use the Superposition Theorem $2\mathrm{.}1\mathrm{.}6$ to decide which of the following statements are true.

A$.y_1+y_2$ solves $(1)$

B$.3y_1$ solves $(1)$

C$.y_1+y_2$ solves $(2)$

D$.-y_1+y_2$ solves $(1)$

E$.5y_2$ solves $(2)$

F$.y_1+2y_2$ solves $(1)$

G$.$ None of the Above

Note: Select all that applies.