y^{'''}+48y^{''}+768y^'+4096y=0

Lösung

y^{^{'''}} + 48 y^{^{''}} + 768 y^{^{'}} + 4096 y = 0

y = c_{1} e^{- 16 t} + c_{2} t e^{- 16 t} + c_{3} t^{2} e^{- 16 t}

Schritte zur Lösung

y^{'''} (t) + 48 y^{''} (t) + 768 y^{'} (t) + 4096 y = 0

Solve linear ODE:

y = c_{1} e^{- 16 t} + c_{2} t e^{- 16 t} + c_{3} t^{2} e^{- 16 t}

y = c_{1} e^{- 16 t} + c_{2} t e^{- 16 t} + c_{3} t^{2} e^{- 16 t}

y^{^{''}} - 5 y^{^{'}} + 6 y = 0, y^{^{'}} (0) = 1

10 y^{^{''}} - 50 y^{^{'}} + 65 y = 0, y (0) = 1, y^{^{'}} (0) = 1

x^{^{''}} - 3 x^{^{'}} + 2 x = 0, x^{0} = 1, x^{^{'}} 0 = - 1

y^{^{''}} - 7 y^{^{'}} + 12 y = 0, y (0) = 2, y^{^{'}} (0) = 3

y^{^{''''}} - y^{^{'''}} - 3 y^{^{''}} + 17 y^{^{'}} - 30 y = 0