y^{''''}+18y^{''}-81y=0

Lösung

y^{^{''''}} + 18 y^{^{''}} - 81 y = 0

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

Schritte zur Lösung

y^{(4)} (t) + 18 y^{''} (t) - 81 y = 0

Solve linear ODE:

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

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

y^{^{''}} + 10 y^{^{'}} + 288 y = 0

(d^{2} + 6) y = 0

y^{^{''}} + 9.82 \cdot y^{^{'}} = 0

y^{^{''}} - 2 y^{^{'}} - 3 y = 0, y (0) = 6, y^{^{'}} (0) = - 6

2 y^{^{''}} + 23 y^{^{'}} - 12 y = 0