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

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

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(dy)/(dx)=((e^{x-y}))/((1+e^x))

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

y = ln (ln (1 + e^{x}) + c_{1})

Solution steps

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

Solve separable ODE:

y = ln (ln (1 + e^{x}) + c_{1})

y = ln (ln (1 + e^{x}) + c_{1})

y^{^{'}} + a \cdot y - b = 0

y = 9 x e^{x}, (0, 0)

y = \frac{1}{2} x, y = \frac{6}{x}, y = 2 x

x \to 5 - lim (\frac{3}{x - 5})

x \to 2 - lim (x - 1)

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