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These are extra credit challenge problems given in my diff. equ. class, and I am in a bit of a rush to figure them out. I tried a few things, but I get lost toward the end.

Here are the problems:

1)

y'''-y''+y'-y=4sin(x)

I did long division with the homogenous equation to find the eigenvalues: 1 , +-i

I am a bit confused as to where to go from there. I need to solve to the particular and homogenous solutions and then add the two to have the general solution, because that is the method we have been working on.

Any help for #1?

2)

IVP y''+y=sec^2(x), y(0)=-1, y'(0)=0

I found eigenvalues of +-i, and got the homogenous solution of C1sin(x)+C2cos(x). Is that correct? How do you solve for the particular solution?

Thanks for the help guys!