Second$-$Order Equation Consider the second$-$order lin

ear differentiaJ equation y$"-$ y$\text{'}-2$y $=0.$

$($a$)$ Verify that y $=$ eu is a solution; then check that

y $=$ e$-1$ is a solution as well.

$($b$)$ Verify that y $=$ Aeu and y $=$ eu $+$ e$-1$ are bothsolutions, where A is any real constant.

$($c$)$ Verify that for any constants A and B$.$ a solution is

y $=$ Aeu $+$ Be$-\text{'}.$

$($d$)$ Detennine vaJues for A and B so that the solution of

part $($c$)$ satisfies bolh y$($O$)=2$ and y$\text{'}($O$)=-5.$