Problem Value: $10$ point$($S$).$ Problem Score: $/5\%.$ Attempts Remaining: $19$ attempts.

Help Entering Answers See Example $2\mathrm{.}5\mathrm{.}3,$ in Section $2\mathrm{.}5,$ in the MTH $235$ Textbook.

$(10$ points$)$

Homework: Non$-$Homogeneous Equations

Consider the differential equation

$y^{\text{'}\text{'}}-3y^{\text{'}}+2y=3sin(4t)$

$($a$)$ Find $r_1,r_2,$ roots of the characteristic polynomial of the equation above.

$$

$($b$)$ Find a set of real$-$valued fundamental solutions to the homogeneous differential equation corresponding to the one above.

$y_1(t)=$

$$

$($c$)$ Find a particular solution $y_p$ of the differential equation above.

$y_p(t)=$

$$