Consider this second$-$order nonhomogeneous differential equation:

$y^{\text{'}\text{'}}2y^{\text{'}}-35y=-6t8$

$($i$)$ Which of the following is the form of the solution of the corresponding homogene are arbitrary real constants.

$y(t)=C_1{e}^{-5t}{C}_2{e}^{7t}$

$y(t)=C_1{e}^{-5t}{C}_{2}t{e}^{-5t}$

$y(t)=C_1{e}^{5t}{C}_{2}t{e}^{5t}$

$y(t)=C_1{e}^{5t}{C}_2{e}^{-7t}$

$y(t)=C_1{e}^{-7t}{C}_{2}t{e}^{-7t}$