y^{''''}-2y^{'''}+4y^{''}+2y^'-5y=0

Lösung

y^{^{''''}} - 2 y^{^{'''}} + 4 y^{^{''}} + 2 y^{^{'}} - 5 y = 0

y = c_{1} e^{- t} + c_{2} e^{t} + e^{t} (c_{3} cos (2 t) + c_{4} sin (2 t))

Schritte zur Lösung

y^{(4)} (t) - 2 y^{'''} (t) + 4 y^{''} (t) + 2 y^{'} (t) - 5 y = 0

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} e^{t} + e^{t} (c_{3} cos (2 t) + c_{4} sin (2 t))

y = c_{1} e^{- t} + c_{2} e^{t} + e^{t} (c_{3} cos (2 t) + c_{4} sin (2 t))

y^{^{''}} - 6 y^{^{'}} + 25 y = 0, y (0) = 2

4 y^{^{''}} + 20 y^{^{'}} + 25 y = 0, y (0) = 1, y^{^{'}} (0) = 2

(D^{3} - 3 D^{2} + 4) y = 0

y^{^{''}} - 24 y^{^{'}} + α y = 0, y (0) = 1, y^{^{'}} (0) = 22

6 \frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - y = 0