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Beliebt Rechnen >

y^{''}+2y^'+2y=e^{-1}

Lösung

y^{^{''}} + 2 y^{^{'}} + 2 y = e^{- 1}

Lösung

y = e^{- t} (c_{1} cos (t) + c_{2} sin (t)) + \frac{1}{2 e}

Schritte zur Lösung

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

Solve linear ODE:

y = e^{- t} (c_{1} cos (t) + c_{2} sin (t)) + \frac{1}{2 e}

y = e^{- t} (c_{1} cos (t) + c_{2} sin (t)) + \frac{1}{2 e}

Graph

Beliebte Beispiele

2y^{''}+3y^'-2y=-8x-13,y(0)=0,y^'(0)=0

2 y^{^{''}} + 3 y^{^{'}} - 2 y = - 8 x - 13, y (0) = 0, y^{^{'}} (0) = 0

2x^{''}-x^'+4x=cos(3t)

2 x^{^{''}} - x^{^{'}} + 4 x = cos (3 t)

y^{''}+9y=5sin(x)

y^{^{''}} + 9 y = 5 sin (x)

y^{''}+7y^'+10y=xe^{-2x}

y^{^{''}} + 7 y^{^{'}} + 10 y = x e^{- 2 x}

y^{''}+y^'-2y=e^{4x}

y^{^{''}} + y^{^{'}} - 2 y = e^{4 x}