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Beliebt Rechnen >

(1+x)(dy)/(dx)-xy=x-x^2

Lösung

(1 + x) \frac{d y}{d x} - x y = x - x^{2}

Lösung

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

Schritte zur Lösung

(1 + x) \frac{d y}{d x} - x y = x - x^{2}

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

(\partial)/(\partial x)(10arccot(x))

\frac{\partial}{\partial x} (10 arccot (x))

derivative 5/(2x)

d er i v a t i v e \frac{5}{2 x}

(\partial)/(\partial x)(1/(sqrt(4pit))e^{-(x^2)/(4t)})

\frac{\partial}{\partial x} (\frac{1}{4 π t} e^{- \frac{x ^{2}}{4 t}})

y (x + 9) + y^{^{'}} = 0

derivative of 5e^{-3x}

\frac{d}{d x} (5 e^{- 3 x})