What is the solution for (dy)/(dx)=((e^{x-y}))/(1+e^x),y(1)=0 ?

The solution for (dy)/(dx)=((e^{x-y}))/(1+e^x),y(1)=0 is y=ln(ln(1+e^x)+1-ln(1+e))

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(dy)/(dx)=((e^{x-y}))/(1+e^x),y(1)=0

\frac{d y}{d x} = \frac{( e ^{x - y} )}{1 + e ^{x}}, y (1) = 0

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

Solution steps

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

Solve separable ODE:

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

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

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\frac{d}{d x} (sin^{2} (a x))

What is the solution for (dy)/(dx)=((e^{x-y}))/(1+e^x),y(1)=0 ?
The solution for (dy)/(dx)=((e^{x-y}))/(1+e^x),y(1)=0 is y=ln(ln(1+e^x)+1-ln(1+e))