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Beliebt Rechnen >

y^{''}-ky=kxe^{-x}

Lösung

y^{^{''}} - k y = k x e^{- x}

Lösung

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

Schritte zur Lösung

y^{''} (x) - k y = k x e^{- x}

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

derivative of 4sqrt(2)

\frac{d}{d x} (42)

y^{''}+9y=e^t,y(0)=0,y^'(0)=0

y^{^{''}} + 9 y = e^{t}, y (0) = 0, y^{^{'}} (0) = 0

integral of e^{(3x+1)}

\int e^{(3 x + 1)} d x

limit as x approaches 27 of (x-27)/(sqrt(x+9-6))

x \to 27 lim (\frac{x - 27}{x + 9 - 6})

a re a 4 x, x^{2}