x^{''}+6x^'+23x=12cos(4t)

解

x^{^{''}} + 6 x^{^{'}} + 23 x = 12 cos (4 t)

x = e^{- 3 t} (c_{1} cos (14 t) + c_{2} sin (14 t)) + \frac{288}{625} sin (4 t) + \frac{84}{625} cos (4 t)

解答ステップ

x^{''} (t) + 6 x^{'} (t) + 23 x = 12 cos (4 t)

線形 ODE を解く:

x = e^{- 3 t} (c_{1} cos (14 t) + c_{2} sin (14 t)) + \frac{288}{625} sin (4 t) + \frac{84}{625} cos (4 t)

x = e^{- 3 t} (c_{1} cos (14 t) + c_{2} sin (14 t)) + \frac{288}{625} sin (4 t) + \frac{84}{625} cos (4 t)