What is the solution for xe^ydy+(x^2+1)/y dx=0 ?

The solution for xe^ydy+(x^2+1)/y dx=0 is y=\W((-x^2-2ln(x)+c_{1})/(2e))+1

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xe^ydy+(x^2+1)/y dx=0

x e^{y} d y + \frac{x ^{2} + 1}{y} d x = 0

y = W (\frac{- x ^{2} - 2 ln ( x ) + c _{1}}{2 e}) + 1

Solution steps

x e^{y} d y + \frac{x ^{2} + 1}{y} d x = 0

Solve separable ODE:

y = W (\frac{- x ^{2} - 2 ln ( x ) + c _{1}}{2 e}) + 1

y = W (\frac{- x ^{2} - 2 ln ( x ) + c _{1}}{2 e}) + 1

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

\frac{d}{d x} (x^{2} sin (x) - x cos (x))

(3 x^{3} + 2 x) (x - 2) (x + 4)

cos (x) d x - sin (y) d y = 0

\int arcsin (d) x d x

What is the solution for xe^ydy+(x^2+1)/y dx=0 ?
The solution for xe^ydy+(x^2+1)/y dx=0 is y=\W((-x^2-2ln(x)+c_{1})/(2e))+1