Consider the non$-$homogeneous differential equation $y^{\text{'}\text{'}}-3y^{\text{'}}=4sinx.$

$($a$)$ Solve the homogeneous part of the differential equation $.$

$(3$ marks$)$

$q,$

$q,$

$q,$

$q,$

$q,$

$q,$

$q,$

$q,$

$($b$)$ Find the particular solution of the differential equation.

$(3$ marks$)$