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})

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})