y'' - 5y' = 2x^3 - 4x^2 -x + 6
The Attempt at a Solution
I first found the m's on the left hand side. They are 0 and 5. I then found the m's on the right hand side. They are 0, 0, 0, and 0. I then wrote my interim equation:
y = C1 + C2e^5x + Ax^4 + Bx^3 + Cx^2 + Dx. Because there already is a 0 on the left hand size for m, then there are x's for each part of the equation on the right side.
This is where I'm confused. I have tried to find the coefficients by finding the first and second derivatives of Yp, but I get very odd numbers when I solve for the variables(B = 14/75 and C = 5.324 for example). Am I on the right track or did I screw up somewhere? We have never been presented with irrational coefficients before (as is the case with C), so I'm thinking I did something wrong somewhere...