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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

x^{^{''}} - 6 x^{^{''}} + x = 0

y^{^{'''}} + 9 y^{^{'}} = 0, y (0) = 5, y^{^{'}} (0) = 4, y^{^{''}} (0) = 3

y^{^{''}} - \frac{2}{5} y = 0

y^{^{''''}} + 2 y^{^{'''}} - 4 y^{^{''}} - 2 y^{^{'}} + \frac{1}{2} y = 0

2.25 y^{^{''}} - 3 y^{^{'}} + y = 0, y (0) = 2, y^{^{'}} (0) = - 1