What is the solution for (2e^y-x)((dy)/(dx))=1 ?

The solution for (2e^y-x)((dy)/(dx))=1 is y=ln((x+sqrt(x^2+c_{1)})/2),y=ln((x-sqrt(x^2+c_{1)})/2)

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(2e^y-x)((dy)/(dx))=1

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

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

Solution steps

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

Solve exact ODE:

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

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

f (x) = - 7 e^{- 3 x} - 6 e^{- 3 x} x

x \to 3 lim (\frac{x ^{2} - 8}{x - 3})

\frac{d}{d x} (x - 3 x^{2} + 8 x^{- 2})

\frac{d y}{d x} = y + 4 y \cdot cos (2 x)

\int - 1728 - x^{3} d x

What is the solution for (2e^y-x)((dy)/(dx))=1 ?
The solution for (2e^y-x)((dy)/(dx))=1 is y=ln((x+sqrt(x^2+c_{1)})/2),y=ln((x-sqrt(x^2+c_{1)})/2)