Given the differential equation: $y"$

$-8y^{\text{'}}15y=-2t^3{e}^{4t}$

a$)$ What is the form of the particular solution to the equation when $6$ is a repeated root? What are the equations to solve for the coefficients.

b$)$ If the equation equaled $t^{2t}cos(3t),$with $3-i$ is a root, what is the form of the particular solution to the equation?