y^{''}-3y^'-4y=8e^tcos(2t)

Lösung

y^{^{''}} - 3 y^{^{'}} - 4 y = 8 e^{t} cos (2 t)

y = c_{1} e^{4 t} + c_{2} e^{- t} - \frac{2}{13} e^{t} sin (2 t) - \frac{10}{13} e^{t} cos (2 t)

Schritte zur Lösung

y^{''} (t) - 3 y^{'} (t) - 4 y = 8 e^{t} cos (2 t)

Solve linear ODE:

y = c_{1} e^{4 t} + c_{2} e^{- t} - \frac{2}{13} e^{t} sin (2 t) - \frac{10}{13} e^{t} cos (2 t)

y = c_{1} e^{4 t} + c_{2} e^{- t} - \frac{2}{13} e^{t} sin (2 t) - \frac{10}{13} e^{t} cos (2 t)

3 y^{^{''}} + 27 y = 2 cos (4 x)

y^{^{'''}} - 3 y^{^{''}} + 4 y^{^{'}} - 12 y = 13 e^{3 x}

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + 2 y = 2 (x + 1)^{2}

y^{^{''}} + 3 y + 2 y = t

y^{^{''}} - 2 y^{^{'}} + 5 y = 8, y (0) = 2, y^{^{'}} (0) = 2