Suppose that Yc = C1(e^(2x)) + C2(cos(3x) + C3(sin(3x) is the complementary solu

Question

Suppose that Yc = C1(e^(2x)) + C2(cos(3x) + C3(sin(3x) is the complementary solution to the differential equation Y''' + (a2)Y" + (a1)Y' +(a0)Y = sin(5x) + 3cos(5x) where a2, a1, and a0 are constants. Find the particular solution to the differential equation.

I tried this problem twice and tried to upload the image of my attempt but it keeps giving me an error. I use chrome. for yp, i used Acos(5x) + Bsin(5x) + Ccos(5x) + Dsin(5x) the first time...and the second time i used only yp = Acos(5x) + Bsin(5x). My first attempt was a total failure whereas in my second attempt, i got A to be 1/125 and B to be -3/125. I dont know if it's right though. Help!

Explanation / Answer

The second one is right.

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