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Beliebt Rechnen >

x^{''}+6x^'+9x=0,x(0)=a,x^'(0)=b

Lösung

x^{^{''}} + 6 x^{^{'}} + 9 x = 0, x (0) = a, x^{^{'}} (0) = b

Lösung

x = a e^{- 3 t} + (b + 3 a) t e^{- 3 t}

Schritte zur Lösung

x^{''} (t) + 6 x^{'} (t) + 9 x = 0

Solve linear ODE:

x = a e^{- 3 t} + (b + 3 a) t e^{- 3 t}

x = a e^{- 3 t} + (b + 3 a) t e^{- 3 t}

Graph

Beliebte Beispiele

y^{''}+14y^'+49y=0,y(0)=-1,y^'(0)=1

y^{^{''}} + 14 y^{^{'}} + 49 y = 0, y (0) = - 1, y^{^{'}} (0) = 1

y^{''''}-3y^{'''}-4y^{''}=0

y^{^{''''}} - 3 y^{^{'''}} - 4 y^{^{''}} = 0

2y^{''}-2y^'+4y=0

2 y^{^{''}} - 2 y^{^{'}} + 4 y = 0

y^{''}+4y^'-5y=0,y(0)=-3,y^'(0)=21

y^{^{''}} + 4 y^{^{'}} - 5 y = 0, y (0) = - 3, y^{^{'}} (0) = 21

x^{''}+6x^'+10x=0

x^{^{''}} + 6 x^{^{'}} + 10 x = 0