y^{''}-2y^'-24y=72e^{2t}

Lösung

y^{^{''}} - 2 y^{^{'}} - 24 y = 72 e^{2 t}

y = c_{1} e^{6 t} + c_{2} e^{- 4 t} - 3 e^{2 t}

Schritte zur Lösung

y^{''} (t) - 2 y^{'} (t) - 24 y = 72 e^{2 t}

Solve linear ODE:

y = c_{1} e^{6 t} + c_{2} e^{- 4 t} - 3 e^{2 t}

y = c_{1} e^{6 t} + c_{2} e^{- 4 t} - 3 e^{2 t}

y^{^{''}} + 49 y = t^{2} cos (7 t) + t e^{(- 7 t)}

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

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} + y = x^{2} e^{x}

\frac{d ^{2} y}{d t ^{2}} + 2 \frac{d y}{d t} - 3 y = e^{t}

y^{^{''}} + 8 y^{^{'}} + 17 y = 6 e^{- 40} cos (t)