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})

\frac{d}{d x} ((7 + x)^{5})

x \to - 0 lim (ln (x))

y = \frac{x ^{2} + 32 x}{8}, x = 4

\frac{2}{s ^{3} ( s ^{2} - 9 )}

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