y^{''}+16y^'+10000y=400sin(200x)

解

y^{^{''}} + 16 y^{^{'}} + 10000 y = 400 sin (200 x)

y = e^{- 8 x} (c_{1} cos (1269 x) + c_{2} sin (1269 x)) - \frac{75}{5689} sin (200 x) - \frac{8}{5689} cos (200 x)

解答ステップ

y^{''} (x) + 16 y^{'} (x) + 10000 y = 400 sin (200 x)

線形 ODE を解く:

y = e^{- 8 x} (c_{1} cos (1269 x) + c_{2} sin (1269 x)) - \frac{75}{5689} sin (200 x) - \frac{8}{5689} cos (200 x)

y = e^{- 8 x} (c_{1} cos (1269 x) + c_{2} sin (1269 x)) - \frac{75}{5689} sin (200 x) - \frac{8}{5689} cos (200 x)