1. The problem statement, all variables and given/known data y''' + y'' - 6y' = 36x 2. Relevant equations y'' + y' - 6y =18x^2 3. The attempt at a solution I've integrated the third order D.E. to get a second order D.E. Solving the characteristic equation, to find a general solution, I get: y = c_1exp(-3x) + c_2exp(2x) However, the answer is given as c_1 + c_2exp(-3x) + c_3exp(2x). Where is the extra term coming from?