y^{''}+7y^'+14y=1096e^{2t}cos(8t)

Lösung

y^{^{''}} + 7 y^{^{'}} + 14 y = 1096 \cdot e^{2 t} \cdot cos (8 t)

y = e^{- \frac{7 t}{2}} (c_{1} cos (\frac{7 t}{2}) + c_{2} sin (\frac{7 t}{2})) + 11 e^{2 t} sin (8 t) - 4 e^{2 t} cos (8 t)

Schritte zur Lösung

y^{''} (t) + 7 y^{'} (t) + 14 y = 1096 \cdot e^{2 t} \cdot cos (8 t)

Solve linear ODE:

y = e^{- \frac{7 t}{2}} (c_{1} cos (\frac{7 t}{2}) + c_{2} sin (\frac{7 t}{2})) + 11 e^{2 t} sin (8 t) - 4 e^{2 t} cos (8 t)

y = e^{- \frac{7 t}{2}} (c_{1} cos (\frac{7 t}{2}) + c_{2} sin (\frac{7 t}{2})) + 11 e^{2 t} sin (8 t) - 4 e^{2 t} cos (8 t)

x^{^{''}} - 2 x^{^{'}} + x = 1 t^{2} e^{t}

y^{^{''}} - 4 y^{^{'}} + 4 y = 8 x^{2} e^{2 x} sin (2 x)

y^{^{''}} - 2 y^{^{'}} - 8 y = - 2 e^{2 x} - 5 x e^{- 4 x} - 2 x

y^{^{''}} - 16 y = 48 t - 24 e^{- 4 t}, y (0) = 0, y^{^{'}} (0) = 16

y^{^{''}} - 8 y^{^{'}} + 16 y = 8 x + 4