y^{''''}-7y^{''}-18y=0

Lösung

y^{^{''''}} - 7 y^{^{''}} - 18 y = 0

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

Schritte zur Lösung

y^{(4)} (t) - 7 y^{''} (t) - 18 y = 0

Solve linear ODE:

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

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

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

y^{^{''}} + 4 y^{^{'}} - 5 y = 0, y (0) = 2, y (0) = 26

64 y^{^{''}} - y = 0, y (- 8) = 1, y^{^{'}} (- 8) = - 1

y^{^{''}} - 6 y^{^{'}} + 13 y = 0, y (0) = 0, y^{^{'}} (0) = - 7

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