Find constants A and B such that the function y = Asin(x) + Bcos(x) satisfies the differential equation y" + y' - 2y = sin(x)
I can find the derivatives just fine, but I'm not sure where to go in order to solve for A or B.
Isolate the sines and cosinesy'(x) = Acosx - Bsinx
y"(x) = -Asinx - bcosx
(-Asinx - Bcosx) + (Acosx - Bsinx) - 2(Asinx + Bcosx) = sinx
From here I'm not sure how to solve for A or B since there are 2 unknowns and only 1 equation