y^{''}+12y^'+24y=4381e^{2t}cos(13t)

解

y^{^{''}} + 12 y^{^{'}} + 24 y = 4381 e^{2 t} cos (13 t)

y = c_{1} e^{2 (3 - 3) t} + c_{2} e^{- 2 (3 + 3) t} + 16 e^{2 t} sin (13 t) - 9 e^{2 t} cos (13 t)

解答ステップ

y^{''} (t) + 12 y^{'} (t) + 24 y = 4381 e^{2 t} cos (13 t)

線形 ODE を解く:

y = c_{1} e^{2 (3 - 3) t} + c_{2} e^{- 2 (3 + 3) t} + 16 e^{2 t} sin (13 t) - 9 e^{2 t} cos (13 t)

y = c_{1} e^{2 (3 - 3) t} + c_{2} e^{- 2 (3 + 3) t} + 16 e^{2 t} sin (13 t) - 9 e^{2 t} cos (13 t)