9y^{''}+6y^'+82y=0

Lösung

9 y^{^{''}} + 6 y^{^{'}} + 82 y = 0

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

Schritte zur Lösung

9 y^{''} (t) + 6 y^{'} (t) + 82 y = 0

Solve linear ODE:

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

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

y^{^{'''}} - 7 y^{^{'}} - 6 y = 0

3 y^{^{''}} + y^{^{'}} - 2 y = 0

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

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

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