y^{''''}+8y^{'''}+21y^{''}+22y^'+8y=0

Lösung

y^{^{''''}} + 8 y^{^{'''}} + 21 y^{^{''}} + 22 y^{^{'}} + 8 y = 0

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

Schritte zur Lösung

y^{(4)} (t) + 8 y^{'''} (t) + 21 y^{''} (t) + 22 y^{'} (t) + 8 y = 0

Solve linear ODE:

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

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

y^{^{''}} + 9 y^{^{'}} + α y = 0, y (0) = 1, y^{^{'}} (0) = - 4

y^{^{''}} + 0.05 y^{^{'}} - 0.0006 y = 0

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = - 1

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = - 5

(d^{2} - 2 d + 5)^{2} y = 0