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Beliebt Rechnen >

y^{''}+2y^'+y=g(t)

Lösung

y^{^{''}} + 2 y^{^{'}} + y = g (t)

Lösung

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

Schritte zur Lösung

y^{''} (t) + 2 y^{'} (t) + y = g (t)

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}+25y=8cos(5x)+12sin(5x)

y^{^{''}} + 25 y = 8 cos (5 x) + 12 sin (5 x)

y^{''}-6y^'+25y=2sin(x/2)-cos(x/2)

y^{^{''}} - 6 y^{^{'}} + 25 y = 2 sin (\frac{x}{2}) - cos (\frac{x}{2})

y^{''}+4y^'+5y=e^{-2x}sin(x)

y^{^{''}} + 4 y^{^{'}} + 5 y = e^{- 2 x} sin (x)

y^{''}+8y^'+20y=100x^2-26xe^x

y^{^{''}} + 8 y^{^{'}} + 20 y = 100 x^{2} - 26 x e^{x}

y^{''}+4y^'+4y=xe^{2x}

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