y^{''}+4y^'+5y=2x-e^{-4x}+sin(2x)

Lösung

y^{^{''}} + 4 y^{^{'}} + 5 y = 2 x - e^{- 4 x} + sin (2 x)

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{2 x}{5} - \frac{8}{25} - \frac{1}{5} e^{- 4 x} + \frac{1}{65} sin (2 x) - \frac{8}{65} cos (2 x)

Schritte zur Lösung

y^{''} (x) + 4 y^{'} (x) + 5 y = 2 x - e^{- 4 x} + sin (2 x)

Solve linear ODE:

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{2 x}{5} - \frac{8}{25} - \frac{1}{5} e^{- 4 x} + \frac{1}{65} sin (2 x) - \frac{8}{65} cos (2 x)

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{2 x}{5} - \frac{8}{25} - \frac{1}{5} e^{- 4 x} + \frac{1}{65} sin (2 x) - \frac{8}{65} cos (2 x)

y^{^{''}} + 25 y = 32 sin (3 x + 2)

y^{^{'''}} - 15 y^{^{''}} + 500 y = e^{10 x}

y^{^{''}} - 3 y^{^{'}} = sin (3 x)

x^{^{''}} - c^{2} x = c cos (c t + a)

y^{^{'''}} - 9 y^{^{''}} + 27 y^{^{'}} - 27 y = 3 e^{3 x}