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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{- 2 x} + c_{2} x e^{- 2 x} + \frac{x}{2} - \frac{1}{2}

Schritte zur Lösung

y^{''} (x) + 4 y^{'} (x) + 4 y = 2 x

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} x e^{- 2 x} + \frac{x}{2} - \frac{1}{2}

y = c_{1} e^{- 2 x} + c_{2} x e^{- 2 x} + \frac{x}{2} - \frac{1}{2}

Graph

Beliebte Beispiele

y^{''''}-16y=xe^{2x}

y^{^{''''}} - 16 y = x e^{2 x}

(D^2-4D+4)y=x^3

(D^{2} - 4 D + 4) y = x^{3}

y^{''}+y=cos(4x)

y^{^{''}} + y = cos (4 x)

y^{''}-8y^'+16y=(e^{-4x})/(1+x^2)

y^{^{''}} - 8 y^{^{'}} + 16 y = \frac{e ^{- 4 x}}{1 + x ^{2}}

y^{''''}-4y^{''}=t^2-e^t

y^{^{''''}} - 4 y^{^{''}} = t^{2} - e^{t}