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Beliebt Rechnen >

x^{''}+16x^'+80x=e^{-8t}

Lösung

x^{^{''}} + 16 x^{^{'}} + 80 x = e^{- 8 t}

Lösung

x = e^{- 8 t} (c_{1} cos (4 t) + c_{2} sin (4 t)) + \frac{1}{16} e^{- 8 t}

Schritte zur Lösung

x^{''} (t) + 16 x^{'} (t) + 80 x = e^{- 8 t}

Solve linear ODE:

x = e^{- 8 t} (c_{1} cos (4 t) + c_{2} sin (4 t)) + \frac{1}{16} e^{- 8 t}

x = e^{- 8 t} (c_{1} cos (4 t) + c_{2} sin (4 t)) + \frac{1}{16} e^{- 8 t}

Graph

Beliebte Beispiele

y^{''}+2y^'-y=t^{-1}*e^t

y^{^{''}} + 2 y^{^{'}} - y = t^{- 1} \cdot e^{t}

y^{''}-2y^'+5y=2x+e^{-x}

y^{^{''}} - 2 y^{^{'}} + 5 y = 2 x + e^{- x}

x^{''}-x^'-12x=e^{4t},x(0)=1,x^'(0)=0

x^{^{''}} - x^{^{'}} - 12 x = e^{4 t}, x (0) = 1, x^{^{'}} (0) = 0

y^{^{''}} - 2 y + y = x

y^{''}+2y^'=-sin(x)

y^{^{''}} + 2 y^{^{'}} = - sin (x)