y^{''}+6y^'+8y=2t-3cos(3t)

Lösung

y^{^{''}} + 6 y^{^{'}} + 8 y = 2 t - 3 cos (3 t)

y = c_{1} e^{- 2 t} + c_{2} e^{- 4 t} + \frac{t}{4} - \frac{3}{16} - \frac{54}{325} sin (3 t) + \frac{3}{325} cos (3 t)

Schritte zur Lösung

y^{''} (t) + 6 y^{'} (t) + 8 y = 2 t - 3 cos (3 t)

Solve linear ODE:

y = c_{1} e^{- 2 t} + c_{2} e^{- 4 t} + \frac{t}{4} - \frac{3}{16} - \frac{54}{325} sin (3 t) + \frac{3}{325} cos (3 t)

y = c_{1} e^{- 2 t} + c_{2} e^{- 4 t} + \frac{t}{4} - \frac{3}{16} - \frac{54}{325} sin (3 t) + \frac{3}{325} cos (3 t)

x^{^{''}} + 10 x^{^{'}} + 25 x = 5 sin (3 t)

y^{^{''}} - 4 y = cos (2 t)

y^{^{'''}} - y^{^{''}} = t^{2} + e^{t}

y^{^{''}} - 2 y^{^{'}} - 15 y = 480 e^{- t}

y^{^{''}} - 4 y^{^{'}} + 4 y = (24 x^{2} + 2) e^{2 x}