What is the solution for e^xydy-(e^{-y}+e^{2x-y})dx=0 ?

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

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e^xydy-(e^{-y}+e^{2x-y})dx=0

e^{x} y d y - (e^{- y} + e^{2 x - y}) d x = 0

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

Solution steps

e^{x} y d y - (e^{- y} + e^{2 x - y}) d x = 0

Solve separable ODE:

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

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

\frac{d}{d x} (lo g_{e} (x^{2} + 1))

\int \frac{e ^{3 x}}{1 - e ^{6 x}} d x

x \to \infty lim (\frac{5 - 2 x ^{\frac{3}{2}}}{3 x - 4})

\int (1 - x) (2 + x^{2}) d x

arctan (\frac{7}{x ^{2}})

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