$(D+1)[u]-(D+1)[v]=e^t$

$(D-1)[u]+(4D+1)[v]=2$

Eliminate $v$ and solve the remaining differential equation for $u.$ Choose the correct answer below.

$A.$ The system $is$ degenerate.

$B.u(t)=C_1+C_2{t}^{-t}+\frac{1}{2}{e}^t+\frac{2}{5}t$

$C.u(t)=C_1+C_2{e}^{-t}+\frac{1}{2}{e}^t+\frac{2}{5}t$

$D.u(t)=C_1+C_2{e}^t+\frac{1}{2}{e}^t+\frac{2}{5}t$

$E.u(t)=C_1{e}^t+C_2{e}^{-t}+\frac{1}{2}{e}^t+\frac{2}{5}t$

Now find $v(t)so$ that $v(t)$ and the solution for $u(t)$ found $in$ the previous step are a general solution $to$ the system $of$ differential equations. Select the correct choice below and, $if$ necessary, fill $in$ the answer box $to$

complete your choice.

$A.v(t)=$

$B.$ The system $is$ degenerate.