Question $3$

Consider the $2nd-$order non$-$homogeneous

differential equation

$y^{\text{'}\text{'}}-4y^{\text{'}}+3y=e^t+t^2.$

What $is$ the complementary $(or$ homogeneous$)$

solution?

$y_c=c_1{e}^t+c_2{t}^2$

$y_c=c_1{e}^{-t}+c_2{e}^{-3t}$

$y_c=c_1{e}^t+c_2{e}^{3t}$

$y_c=c_1{e}^t+c_2{e}^{-3t}$

$y_c=c_1{e}^{-t}+c_2{e}^{3t}$