x^{'''}+3x^{''}+3x^'+x=0

Lösung

x^{^{'''}} + 3 x^{^{''}} + 3 x^{^{'}} + x = 0

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

Schritte zur Lösung

x^{'''} (t) + 3 x^{''} (t) + 3 x^{'} (t) + x = 0

Solve linear ODE:

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

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

y^{^{''}} - 2 y^{^{'}} - 8 y = 0, y (0) = a, y^{^{'}} (0) = - 8

y^{^{''}} + 3 y^{^{'}} = 0, y^{^{'}} (0) = 0, y (0) = 0

2 y^{^{''}} + 12 y^{^{'}} + 24 y = 0, y (0) = 1, y^{^{'}} (0) = 4

4 y^{^{''}} - 4 y^{^{'}} + y = 0, y (0) = 1, y^{^{'}} (0) = - 1

y^{^{''}} - 10 y^{^{'}} + 25 y = 0, y (0) = - 6, y^{^{'}} (0) = - 32