I was doing this question y''+3y'=cos(x)+1 and when finding the particular solution wasnt sure if I could use y=Acos(x)+Bsin(x) becuase of the +1. Is this the right method for this question?
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Yes, you do for the $\displaystyle \cos x$ but you'll also need $\displaystyle y_p = Ax $ for the 1 term.
So I am finding two particular solutions?
Yes - one for each of the nonhomogeneous terms (the two different types of terms).
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