Consider the differential equation

$y^{\text{'}\text{'}}-5y^{\text{'}}+4y=4sin(4t)$

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

$r_1,r_2=$

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

$y_1(t)=$

$y_2(t)=$

$(c)$ Find a particular solution $y_{p}of$ the differential equation above.

$y_p(t)=$