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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

y^{^{''}} + 6 y^{^{'}} + 9 y = 2 e^{- 2 x} + sin (2 x)

y^{^{''}} + 49 y = cos (7 t), y (0) = - 5, y^{^{'}} (0) = - 56

y^{^{''}} + 5 y + 4 = 0, y (0) = 1, y^{^{'}} (0) = 1

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

y^{^{''}} + 4 y^{^{'}} = t^{2} + 2 e^{t}, y (0) = 0, y^{^{'}} (0) = 1