x^{'''}+5x^{''}-25x^'-125x=0

Lösung

x^{^{'''}} + 5 x^{^{''}} - 25 x^{^{'}} - 125 x = 0

x = c_{1} e^{5 t} + c_{2} e^{- 5 t} + c_{3} t e^{- 5 t}

Schritte zur Lösung

x^{'''} (t) + 5 x^{''} (t) - 25 x^{'} (t) - 125 x = 0

Solve linear ODE:

x = c_{1} e^{5 t} + c_{2} e^{- 5 t} + c_{3} t e^{- 5 t}

x = c_{1} e^{5 t} + c_{2} e^{- 5 t} + c_{3} t e^{- 5 t}

y^{^{''}} - 12 y^{^{'}} + 35 y = 0, y (0) = e^{k x}

\frac{d ^{3} y}{d x ^{3}} + 5 y = 0

y^{^{''}} + 5 y^{^{'}} - 14 y = 0, y^{^{'}} (0) = 56

y^{^{''}} - 2 y^{^{'}} + 5 y = 0, y^{^{'}} (0) = 2, y (0) = 1

y^{^{''}} + 64 y = 0, y (0) = 0, y^{^{'}} (0) = \frac{64}{5}