(d^2+6d+10)y=3xe^{-3x}-2e^{3x}cos(x)

Lösung

(d^{2} + 6 d + 10) y = 3 x e^{- 3 x} - 2 e^{3 x} cos (x)

y = e^{- 3 x} (c_{1} cos (x) + c_{2} sin (x)) + 3 e^{- 3 x} x - \frac{1}{60} e^{3 x} sin (x) - \frac{1}{20} e^{3 x} cos (x)

Schritte zur Lösung

(d^{2} + 6 d + 10) y = 3 x e^{- 3 x} - 2 e^{3 x} cos (x)

Solve linear ODE:

y = e^{- 3 x} (c_{1} cos (x) + c_{2} sin (x)) + 3 e^{- 3 x} x - \frac{1}{60} e^{3 x} sin (x) - \frac{1}{20} e^{3 x} cos (x)

y = e^{- 3 x} (c_{1} cos (x) + c_{2} sin (x)) + 3 e^{- 3 x} x - \frac{1}{60} e^{3 x} sin (x) - \frac{1}{20} e^{3 x} cos (x)

y^{^{''}} + 2 y^{^{'}} - 8 y = 6 e^{- 3 x} - e^{- x}

y^{^{''}} + y = \frac{1}{cos ( t )}

y^{^{''}} - 6 y^{^{'}} + 9 y = 3 x^{2} + 4 e^{4 x}

y^{^{''}} + 4 y^{^{'}} + 3 y = e^{- 3 x}

y^{^{''}} - y^{^{'}} - 2 y = 1