I have 3 non-homogeneous differential equations. The first i have done myself and believe to be correct, but can someone just confirm. The second and third i just need some guidance on what form the particular solution will take and the rest i will try to do myself:

1) y" - y' - 12y = e^6x here i used yp = ce^6x and got the general solution as yh = Ae^-3x + Be^4x + e^6x/18

2) y" - y' -6y = e^-x + 12x and yp = ???? y(0)=1, y'(0)=-2

3) y" + 2y' + 5y = cos3x and yp = ???? y(0)=1, y'(0)=0