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

Lösung

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

y = c_{1} e^{- 2 t} + c_{2} t e^{- 2 t} + \frac{9}{25} sin (t) - \frac{12}{25} cos (t) + \frac{1}{8} e^{2 t}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{- 2 t} + c_{2} t e^{- 2 t} + \frac{9}{25} sin (t) - \frac{12}{25} cos (t) + \frac{1}{8} e^{2 t}

y = c_{1} e^{- 2 t} + c_{2} t e^{- 2 t} + \frac{9}{25} sin (t) - \frac{12}{25} cos (t) + \frac{1}{8} e^{2 t}

y^{^{''}} + 2 y^{^{'}} - 3 y = 12 e^{x} - 6

1 q^{^{''}} + 8 q^{^{'}} + \frac{1}{0.05} q = 80 t

(D + 1)^{2} y = x^{2} e^{- x}

y^{^{''}} - 5 y^{^{'}} + 6 y = e^{t}, y (0) = 1, y^{^{'}} (0) = 1

\frac{d ^{2} y}{d x ^{2}} - 8 \frac{d y}{d x} + 2 y = x e^{x}