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

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

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(y-x)e^x+(1+e^x)y^'=0,y(1)=1

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

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

Solution steps

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

Solve exact ODE:

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

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

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