16y^{''}+8y^'+5y=0

Lösung

16 y^{^{''}} + 8 y^{^{'}} + 5 y = 0

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

Schritte zur Lösung

16 y^{''} (t) + 8 y^{'} (t) + 5 y = 0

Solve linear ODE:

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

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

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

(D^{2} + 4 D + 5) y = 0

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

y^{^{''''}} + 4 y^{^{'''}} + 6 y^{^{''}} + 4 y^{^{'}} + y = 0

11 x^{^{''}} + 112.5 x = 0