1/2 x^{''}+2x^'+4x=20cos(t)

Lösung

\frac{1}{2} x^{^{''}} + 2 x^{^{'}} + 4 x = 20 cos (t)

x = e^{- 2 t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + \frac{32}{13} sin (t) + \frac{56}{13} cos (t)

Schritte zur Lösung

\frac{1}{2} x^{''} (t) + 2 x^{'} (t) + 4 x = 20 cos (t)

Solve linear ODE:

x = e^{- 2 t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + \frac{32}{13} sin (t) + \frac{56}{13} cos (t)

x = e^{- 2 t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + \frac{32}{13} sin (t) + \frac{56}{13} cos (t)

2 y^{^{''}} + 8 y^{^{'}} + 80 y = 40 cos (8 x)

y^{^{''''}} - 4 y^{^{''}} = x^{2} + 3 e^{x}

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

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

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