y^{''}+6y^'+16y=0

Lösung

y^{^{''}} + 6 y^{^{'}} + 16 y = 0

y = e^{- 3 t} (c_{1} cos (7 t) + c_{2} sin (7 t))

Schritte zur Lösung

y^{''} (t) + 6 y^{'} (t) + 16 y = 0

Solve linear ODE:

y = e^{- 3 t} (c_{1} cos (7 t) + c_{2} sin (7 t))

y = e^{- 3 t} (c_{1} cos (7 t) + c_{2} sin (7 t))

5 y^{^{''}} + 20 y = 0

(D^{4} - 2 D^{2} + 4) y = 0

4 y^{^{''}} - 8 y^{^{'}} + 3 y = 0, y (0) = 2, y^{^{'}} (0) = 1

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

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