1. The problem statement, all variables and given/known data y"' -9y" +18y" = 30ex. Does not matter what the initial conditions are for my question. 2. Relevant equations N/A 3. The attempt at a solution So I factored out the equation and got: r*(r2 - 9r + 18) Which gives roots r = 0, r = 3, r = 6. Which gives me the general solution: y(x) = C0*1 + C1e3x + C2e6x Is the above general solution correct? Next question I have is whether I solved for the yp correctly. yp = A*ex yp' = A*ex yp" = A*ex yp'" = A*ex which by plugging into the equation will give. A*ex - 9A*ex + 18A*ex = 30ex which gives 10A*ex = 30ex which gives A = 3. Which means my general solution should be. y(x) = y(x) = C0*1 + C1e3x + C2e6x +3*ex Is all this correct because I am trying to solve for the "C0, C1, etc." and I want to be absolutely sure that the base I am working with is correct and that my error is just a miscalculation with the initial conditions. Thanks.