D^2(D^2-4D+5)^3y=0

解

D^{2} (D^{2} - 4 D + 5)^{3} y = 0

y = c_{1} + c_{2} x + e^{2 x} (c_{3} cos (x) + c_{4} sin (x)) + x e^{2 x} (c_{5} cos (x) + c_{6} sin (x)) + x^{2} e^{2 x} (c_{7} cos (x) + c_{8} sin (x))

解答ステップ

D^{2} (D^{2} - 4 D + 5)^{3} y = 0

線形 ODE を解く:

y = c_{1} + c_{2} x + e^{2 x} (c_{3} cos (x) + c_{4} sin (x)) + x e^{2 x} (c_{5} cos (x) + c_{6} sin (x)) + x^{2} e^{2 x} (c_{7} cos (x) + c_{8} sin (x))

y = c_{1} + c_{2} x + e^{2 x} (c_{3} cos (x) + c_{4} sin (x)) + x e^{2 x} (c_{5} cos (x) + c_{6} sin (x)) + x^{2} e^{2 x} (c_{7} cos (x) + c_{8} sin (x))