1. The problem statement, all variables and given/known data y4 - 6y3 + 9y2 y(0) = 19; y'(0) = 16; y"(0) = 9; y"'(0) = 0 2. Relevant equations N/A 3. The attempt at a solution Factored out the equation and obtained the following roots. r2(r2-3) = 0 which gives r = 0 and r =3. Using those roots, I make the following general solution. y(x) = j*e3x + k*x*e3x + L*k*x2*e3x I am assuming since one of the roots is zero then the solution will not have to have add i*e0t. I am also assuming since this is a fourth order equation that I will need to solve for n=4 variables and that this is the form in which I should tackle it. Am I mistaken in my assumptions?