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Beliebt Rechnen >

y^{'''}+6y^{''}+12y^'+8y=0

Lösung

y^{^{'''}} + 6 y^{^{''}} + 12 y^{^{'}} + 8 y = 0

Lösung

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

Schritte zur Lösung

y^{'''} (t) + 6 y^{''} (t) + 12 y^{'} (t) + 8 y = 0

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

(D^{3} + 1) y = 0

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

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

y^{'''}-5y^{''}+17y^'-13y=0

y^{^{'''}} - 5 y^{^{''}} + 17 y^{^{'}} - 13 y = 0

y^{''}+22y^'+122y=0,y(0)=1,y^'(0)=0

y^{^{''}} + 22 y^{^{'}} + 122 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{''}-4y^'+13y=0,y(0)=-5,y^'(0)=-1

y^{^{''}} - 4 y^{^{'}} + 13 y = 0, y (0) = - 5, y^{^{'}} (0) = - 1