(D^2-4D+4)y=e^{-4x}+5cos(3x)

Lösung

(D^{2} - 4 D + 4) y = e^{- 4 x} + 5 cos (3 x)

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{1}{36} e^{- 4 x} - \frac{60}{169} sin (3 x) - \frac{25}{169} cos (3 x)

Schritte zur Lösung

(D^{2} - 4 D + 4) y = e^{- 4 x} + 5 cos (3 x)

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{1}{36} e^{- 4 x} - \frac{60}{169} sin (3 x) - \frac{25}{169} cos (3 x)

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{1}{36} e^{- 4 x} - \frac{60}{169} sin (3 x) - \frac{25}{169} cos (3 x)

\frac{d ^{2} y}{d x ^{2}} + 6 \frac{d y}{d x} + 10 y = 50 x

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

y^{^{''}} + 8 y^{^{'}} + 16 y = 4 e^{- 4 t}

y^{^{''}} - 3 y^{^{'}} + 2 y = 3 cos (3 t), y (0) = 2, y^{^{'}} (0) = 3

y^{^{''}} + 16 y = 11 sec^{2} (4 t)