Find the linear, nonhomogeneous differential equation with constant coefficients whose solution is

$y(t)=c_1{e}^t+c_2{e}^{2t}-3t{e}^t+cost-\frac{e^{-t}}{2}$

A$)y^{\text{'}\text{'}}+3y^{\text{'}}+2y=3e^t+3cost-3sint-3e^{-t}$

B$)y^{\text{'}\text{'}}-3y^{\text{'}}+2y=3e^t+cost+3sint-3e^{-t}$

C$)y^{\text{'}\text{'}}+3y^{\text{'}}+2y=3t{e}^t+cost-3sint$

D$)y^{\text{'}\text{'}}-2y^{\text{'}}-3y=-3e^t+3e^{-t}+sint$

E$)y^{\text{'}\text{'}}-3y^{\text{'}}+2y=-3e^t-cost+3sint-\frac{5}{2}{e}^{-t}$