1/8 y^{''}+y^'+2y=0

Lösung

\frac{1}{8} y^{^{''}} + y^{^{'}} + 2 y = 0

y = c_{1} e^{- 4 t} + c_{2} t e^{- 4 t}

Schritte zur Lösung

\frac{1}{8} y^{''} (t) + y^{'} (t) + 2 y = 0

Solve linear ODE:

y = c_{1} e^{- 4 t} + c_{2} t e^{- 4 t}

y = c_{1} e^{- 4 t} + c_{2} t e^{- 4 t}

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

y^{^{'''}} - 12 y^{^{''}} - 28 y^{^{'}} + 480 y = 0

9 y^{^{''}} + 24 y + 16 y = 0

D^{2} (D - 1) y = 0

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