y^{''}+7y^'+10y=100sin(10t)

Lösung

y^{^{''}} + 7 y^{^{'}} + 10 y = 100 sin (10 t)

y = c_{1} e^{- 2 t} + c_{2} e^{- 5 t} - \frac{9}{13} sin (10 t) - \frac{7}{13} cos (10 t)

Schritte zur Lösung

y^{''} (t) + 7 y^{'} (t) + 10 y = 100 sin (10 t)

Solve linear ODE:

y = c_{1} e^{- 2 t} + c_{2} e^{- 5 t} - \frac{9}{13} sin (10 t) - \frac{7}{13} cos (10 t)

y = c_{1} e^{- 2 t} + c_{2} e^{- 5 t} - \frac{9}{13} sin (10 t) - \frac{7}{13} cos (10 t)

y^{^{''}} + 2 y^{^{'}} + 2 y = 2 t^{2} e^{- t} sin (t)

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

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

y^{^{''}} + 2 y^{^{'}} = 1 + (t - 2), y (0) = 0, y^{^{'}} (0) = 1

4 x^{^{''}} + 85 x = cos (6 t)