x^{''}+4x^'+13x=5cos(2t)

Lösung

x^{^{''}} + 4 x^{^{'}} + 13 x = 5 cos (2 t)

x = e^{- 2 t} (c_{1} cos (3 t) + c_{2} sin (3 t)) + \frac{8}{29} sin (2 t) + \frac{9}{29} cos (2 t)

Schritte zur Lösung

x^{''} (t) + 4 x^{'} (t) + 13 x = 5 cos (2 t)

Solve linear ODE:

x = e^{- 2 t} (c_{1} cos (3 t) + c_{2} sin (3 t)) + \frac{8}{29} sin (2 t) + \frac{9}{29} cos (2 t)

x = e^{- 2 t} (c_{1} cos (3 t) + c_{2} sin (3 t)) + \frac{8}{29} sin (2 t) + \frac{9}{29} cos (2 t)

y^{^{''}} - 4 y^{^{'}} + 4 y = e^{- x}

y^{^{''}} - 3 y^{^{'}} + 2 y = 2 e^{- 3 t}, y (0) = 0, y^{^{'}} (0) = 1

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

y^{^{''}} + 4 y = e^{- 4 t}, y (0) = 2

y^{^{''}} + 25 y = 40 cos (5 t), y (0) = y