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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

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

3 y \frac{d y}{d x} = 11 x^{2}

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

d x + x y d y = y^{2} d x + y d y, y (2) = 3

\frac{d y}{d t} = \frac{2 t}{1 + 2 y}, y (2) = 0

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