Thread: Homogeneous equations with constant coefficients

y^(4) + 18y'' + 81y = 0

Find the general solution of the differential equation

your cahracteristic eqn is L^4 + 18L^2 + 81 = 0

(L^2 +9)^2 = 0 L = 3i (recall you only need one root)

so you solutions are cos(3x),sin(3x),xcos(3x), and xsin(3x)