y^{''''}+2y^{'''}+10y^{''}+18y^'+9y=0

Lösung

y^{^{''''}} + 2 y^{^{'''}} + 10 y^{^{''}} + 18 y^{^{'}} + 9 y = 0

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

Schritte zur Lösung

y^{(4)} (t) + 2 y^{'''} (t) + 10 y^{''} (t) + 18 y^{'} (t) + 9 y = 0

Solve linear ODE:

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

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

3 y^{^{''}} - 5 y^{^{'}} = 0

y^{^{''}} - 2 y^{^{'}} + 2 y = 0, y (π) = e^{π}, y^{^{'}} (π) = 0

y^{^{'''}} - 9 y^{^{''}} + 23 y^{^{'}} - 15 y = 0

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

6 y^{^{''}} - 5 y^{^{'}} + y = 0, y (0) = 4, y^{^{'}} (0) = 0