y^{''}-3y^'=8e^{2t}-2e^{-t}

Lösung

y^{^{''}} - 3 y^{^{'}} = 8 e^{2 t} - 2 e^{- t}

y = c_{1} e^{3 t} + c_{2} - 4 e^{2 t} - \frac{1}{2} e^{- t}

Schritte zur Lösung

y^{''} (t) - 3 y^{'} (t) = 8 e^{2 t} - 2 e^{- t}

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} - 4 e^{2 t} - \frac{1}{2} e^{- t}

y = c_{1} e^{3 t} + c_{2} - 4 e^{2 t} - \frac{1}{2} e^{- t}

y^{^{''}} - 2 y^{^{'}} + y = t

y^{^{''}} - 4 y^{^{'}} = 8 e^{6 x} (x - 1)

y^{^{''}} - y = e^{x} cos (x)

y^{^{'''}} - y^{^{'}} = 7 t

y^{^{'''}} + 4 y^{^{'}} = t