The general solution to the x power of the differential equation y "+ 3Y + 2Y = e

The general solution to the x power of the differential equation y "+ 3Y + 2Y = e

The problem should be y "+ 3Y '+ 2Y = e ^ x? The characteristic equation is R ^ 2 + 3R + 2 = 0, and R = - 1, - 2 is the general solution of homogeneous equation. Y1 = C1E ^ (- x) + c2e ^ (- 2x) let the special solution y * = AE ^ x, and substitute it into the equation to get: AE ^ x + 3aE ^ x + 2ae ^ x = e ^ x, that is, 6ae ^ x = e ^ x, and 6A = 1A = 1 / 6, so the general solution of the original equation y = Y1 + y * = C1E ^ (- x) + c2e ^ (- 2x) +