Method of undetermined coefficients

Using the Method of Undetermined Coefficients
Find the solution to the following differential equation:

$y''-6y'+5y=2e^{3x}$
With initial values $y(0)=-\frac{1}{2}$ , and $y' (0)=-\frac{1}{2}$
Find the solution to the following differential equation:

$y''+y'-6y=4\sin(2x)$
With initial values $y(0)=\frac{12}{13}$ , and $y' (0)=-\frac{10}{13}$
Find the solution to the following differential equation:

$y''+y'-6y=-12x^3+3x^2+\frac{19}{6}$
With initial values $y(0)=3$ and $y' (0)=-1$
Find the general solution to the following differential equation:
$y''+2y'+y=xe^{3x}+5\cos(3x)$