x^{''}+2x^'+41x=11cos(6t)

解

x^{^{''}} + 2 x^{^{'}} + 41 x = 11 cos (6 t)

x = e^{- t} (c_{1} cos (210 t) + c_{2} sin (210 t)) + \frac{132}{169} sin (6 t) + \frac{55}{169} cos (6 t)

解答ステップ

x^{''} (t) + 2 x^{'} (t) + 41 x = 11 cos (6 t)

線形 ODE を解く:

x = e^{- t} (c_{1} cos (210 t) + c_{2} sin (210 t)) + \frac{132}{169} sin (6 t) + \frac{55}{169} cos (6 t)

x = e^{- t} (c_{1} cos (210 t) + c_{2} sin (210 t)) + \frac{132}{169} sin (6 t) + \frac{55}{169} cos (6 t)