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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{- 2 x} + c_{2} x e^{- 2 x} + \frac{2 e ^{- 2 x} x ^{2} ln ( x ) - 3 e ^{- 2 x} x ^{2}}{4}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} x e^{- 2 x} + \frac{2 e ^{- 2 x} x ^{2} ln ( x ) - 3 e ^{- 2 x} x ^{2}}{4}

y = c_{1} e^{- 2 x} + c_{2} x e^{- 2 x} + \frac{2 e ^{- 2 x} x ^{2} ln ( x ) - 3 e ^{- 2 x} x ^{2}}{4}

Graph

Beliebte Beispiele

derivative f(x)= 1/(7-x)

d er i v a t i v e f (x) = \frac{1}{7 - x}

derivative of h(sqrt(x))

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d er i v a t i v e f (x) = \frac{9}{x}

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\frac{d y}{d x} = \frac{1}{6} y cos^{2} (y)

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\int 11 (tan (x)) (ln (cos (x))) d x