(d^3-7d-6)y=2e^xcos(x/2)

Lösung

(d^{3} - 7 d - 6) y = 2 e^{x} cos (\frac{x}{2})

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + c_{3} e^{3 x} - \frac{16}{629} e^{x} sin (\frac{x}{2}) - \frac{96}{629} e^{x} cos (\frac{x}{2})

Schritte zur Lösung

(d^{3} - 7 d - 6) y = 2 e^{x} cos (\frac{x}{2})

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + c_{3} e^{3 x} - \frac{16}{629} e^{x} sin (\frac{x}{2}) - \frac{96}{629} e^{x} cos (\frac{x}{2})

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + c_{3} e^{3 x} - \frac{16}{629} e^{x} sin (\frac{x}{2}) - \frac{96}{629} e^{x} cos (\frac{x}{2})

y^{^{''}} + 5 y^{^{'}} + 6 y = 3 e^{- 2 x}

y^{^{''}} - 4 y - 12 y = 12 t

y^{^{''}} + y^{^{'}} - 6 = 2 x

y^{^{''}} - 2 y^{^{'}} - 3 y = 2 x e^{3 x}

y^{^{''}} - 2 y^{^{'}} = 8 x