x^{''}-x=3e^{-2t}

Lösung

x^{^{''}} - x = 3 e^{- 2 t}

x = c_{1} e^{t} + c_{2} e^{- t} + e^{- 2 t}

Schritte zur Lösung

x^{''} (t) - x = 3 e^{- 2 t}

Solve linear ODE:

x = c_{1} e^{t} + c_{2} e^{- t} + e^{- 2 t}

x = c_{1} e^{t} + c_{2} e^{- t} + e^{- 2 t}

y^{^{''''}} - y = 7 t + cos (t)

y^{^{''}} + 3 y^{^{'}} + 2 y = 1, y (0) = 0, y^{^{'}} (0) = 0

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

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

y^{^{''}} + 16 y = 16, y (0) = 1, y^{^{'}} (0) = - 4