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

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

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y^'=(e^{x+y})/(1+e^x),y(1)=0

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

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

Solution steps

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