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Beliebt Rechnen >

x^{''}+10x^'+16x=0,x(0)=1,x^'(0)=-13

Lösung

x^{^{''}} + 10 x^{^{'}} + 16 x = 0, x (0) = 1, x^{^{'}} (0) = - 13

Lösung

x = (1 - \frac{11}{6}) e^{- 2 t} + \frac{11}{6} e^{- 8 t}

Schritte zur Lösung

x^{''} (t) + 10 x^{'} (t) + 16 x = 0

Solve linear ODE:

x = (1 - \frac{11}{6}) e^{- 2 t} + \frac{11}{6} e^{- 8 t}

x = (1 - \frac{11}{6}) e^{- 2 t} + \frac{11}{6} e^{- 8 t}

Graph

Beliebte Beispiele

6y^{''}-5y^'+y=0,y(0)=e^{x/2}

6 y^{^{''}} - 5 y^{^{'}} + y = 0, y (0) = e^{\frac{x}{2}}

y^{'''}+2y^{''}-20y^'+24y=0

y^{^{'''}} + 2 y^{^{''}} - 20 y^{^{'}} + 24 y = 0

y^{''}-8y^{''}+16y=0

y^{^{''}} - 8 y^{^{''}} + 16 y = 0

6y^{''}+(-5)y^'+y=0,y(0)=4,y^'(0)=0

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

y^{''}-2y^'+13y=0

y^{^{''}} - 2 y^{^{'}} + 13 y = 0