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

Lösung

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)

Schritte zur Lösung

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

Solve linear ODE:

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)

(d^{2} - 4) y = e^{- 3 x} sin (e^{- x})

(D^{2} - 6 D + 9) y = 1 + x + x^{2}

y^{^{''}} + 3 y^{^{'}} + 13 y = 52, y (0) = 2, y^{^{'}} (0) = 1

y^{^{''}} + 2 y^{^{'}} - 3 y = 5 e^{2 x}, y (0) = 0, y^{^{'}} (0) = 5

y^{^{''}} + 3 y^{^{'}} + 2 y = 10 e^{x}