y^{''}-3y^'-4y=8e^xcos(2x)

Lösung

y^{^{''}} - 3 y^{^{'}} - 4 y = 8 e^{x} cos (2 x)

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

Schritte zur Lösung

y^{''} (x) - 3 y^{'} (x) - 4 y = 8 e^{x} cos (2 x)

Solve linear ODE:

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

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

y^{^{''}} + 6 y^{^{'}} + 5 y = - 1020 sin (3 t)

(D^{2} + 4 D + 8) y = 4 sin (2 x)

y^{^{''}} + 9 y = 2 t^{2} - 2, y (0) = 0, y^{^{'}} (0) = - 8

y^{^{'''}} + 3 y^{^{''}} - y^{^{'}} - 3 y = 3 x - 14

y^{^{''}} - 16 y^{^{'}} + 64 y = - \frac{2}{3 x} e^{8 x}