Consider the differential equation

y$^(\text{'}\text{'})-2$y$^(\text{'})-3$y$=0$

Part $1$: Checking for Solutions

$?$ Course Help

A$.$ e$^(3$t$)$

B$.$ e$^(4$t$)$

C$.$ e$^(-$t$)$

D$.$ e$^(-2$t$)$

E$.$ None of the Above

Note: Select all that applies.

Part $2$: Fundamental Solutions

$($b$)$ Use the solution in part $($a$)$ and properties of linear operators to determine which of these pair of functions form a fundamental set of solutions of the

differential equation above.

A$.6$e$^(3$t$)$ and $2$e$^(-$t$)$

B$.$ e$^(4$t$)$ and e$^(-$t$)$

C$.$ e$^(3$t$)$ and e$^(-$t$)$

D$.$ e$^(3$t$)$ and e$^(-2$t$)$

E$.$ te$^(3$t$)$ and e$^(-$t$)$

F$.2$e$^(3$t$)+3$e$^(-$t$),$ and e$^(-$t$)$

G$.$ None of the Above

Note: Select all that applies.