y^{''}+10y^'+16y=3cos(5t)+4sin(5t)

Lösung

y^{^{''}} + 10 y^{^{'}} + 16 y = 3 cos (5 t) + 4 sin (5 t)

y = c_{1} e^{- 2 t} + c_{2} e^{- 8 t} + \frac{114}{2581} sin (5 t) - \frac{227}{2581} cos (5 t)

Schritte zur Lösung

y^{''} (t) + 10 y^{'} (t) + 16 y = 3 cos (5 t) + 4 sin (5 t)

Solve linear ODE:

y = c_{1} e^{- 2 t} + c_{2} e^{- 8 t} + \frac{114}{2581} sin (5 t) - \frac{227}{2581} cos (5 t)

y = c_{1} e^{- 2 t} + c_{2} e^{- 8 t} + \frac{114}{2581} sin (5 t) - \frac{227}{2581} cos (5 t)

2 y^{^{''}} + 2 y = 2 cos^{2} (x)

y^{^{''}} + 4 y^{^{'}} + 5 y = 35 e^{- 4 x}, y (0) = - 2

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

y^{^{''}} - 2 y^{^{'}} = 1, y (0) = 2, y^{^{'}} (0) = 1

y^{^{''}} - y^{^{'}} + 14 y = 5 + e^{\frac{x}{2}}