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

Lösung

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

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

Schritte zur Lösung

x^{(4)} (t) - x = 0

Solve linear ODE:

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

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

y^{^{'''}} - 6 y^{^{''}} + 11 y^{^{'}} = 0

81 y^{^{''}} - 234 y^{^{'}} + 169 y = 0

(d^{2} + 4 d + 4) y = 0

y^{^{'''}} - 15 y^{^{''}} + 66 y^{^{'}} - 80 y = 0

y^{^{''}} + k^{2} y^{^{'}} = 0