y^{''}-3y^'+2y=e^{-4t}

Lösung

y^{^{''}} - 3 y^{^{'}} + 2 y = e^{- 4 t}

y = c_{1} e^{2 t} + c_{2} e^{t} + \frac{1}{30} e^{- 4 t}

Schritte zur Lösung

y^{''} (t) - 3 y^{'} (t) + 2 y = e^{- 4 t}

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{t} + \frac{1}{30} e^{- 4 t}

y = c_{1} e^{2 t} + c_{2} e^{t} + \frac{1}{30} e^{- 4 t}

y^{^{''}} - 5 y^{^{'}} + 6 y = x^{2}

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

y^{^{''}} + y^{^{'}} + y = 2 cos (2 x) - 3 sin (2 x)

y^{^{''}} + 6 y^{^{'}} + 12 y = 763 e^{2 t} cos (7 t)

y^{^{''}} + y = \frac{2}{cos ( x )}, y (0) = 2, y^{^{'}} (0) = 2