1. The problem statement, all variables and given/known data Solve the given differential equation using the annihilator method: (D-3)(D+2)y=x^2e^x 2. Relevant equations D=dy/dx 3. The attempt at a solution I think the annihilator would be (D-1)^3. so the solution would be in the form: y = Ae^x + Bxe^x + C(x^2)e^x + De^(3x) +Ee^(-2x) Solving for the particular solution yields: Ae^x+Bxe^x+C(x^2)e^x = (x^2)(e^x) Am I solving this correctly, and if so, where do I go from here? Thanks a bunch, John 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution
Everything looks fine, so far. Using your particular solution, y = Ae^x + Bxe^x + Cx^2e^x, calculate y' and y'' and substitute into your differential equation to find A, B, and C. Your differential equation is y'' - y' - 6y = x^2e^x Your general solution will still involve undetermined coefficients for the e^(3x) and e^(-2x) terms unless you have some initial conditions.