5y^{''}+88y^'+240y=82sin(6x)

解

5 y^{^{''}} + 88 y^{^{'}} + 240 y = 82 sin (6 x)

y = c_{1} e^{\frac{4 ( 46 - 11 ) x}{5}} + c_{2} e^{- \frac{4 ( 11 + 46 ) x}{5}} + \frac{205}{11766} sin (6 x) - \frac{902}{5883} cos (6 x)

解答ステップ

5 y^{''} (x) + 88 y^{'} (x) + 240 y = 82 sin (6 x)

線形 ODE を解く:

y = c_{1} e^{\frac{4 ( 46 - 11 ) x}{5}} + c_{2} e^{- \frac{4 ( 11 + 46 ) x}{5}} + \frac{205}{11766} sin (6 x) - \frac{902}{5883} cos (6 x)

y = c_{1} e^{\frac{4 ( 46 - 11 ) x}{5}} + c_{2} e^{- \frac{4 ( 11 + 46 ) x}{5}} + \frac{205}{11766} sin (6 x) - \frac{902}{5883} cos (6 x)