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

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

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

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

10 + \frac{50 t}{2 t ^{2} + 9}

x \to - 2 lim (\frac{1}{2})

\frac{- 3 e ^{6 - 3 s}}{( s - 2 ) ( s - 3 ) ( s + 2 )}

h \to 0 lim ((x + h)^{3} - x^{3})

\frac{\partial}{\partial t} (2 e^{s i n (x + 2 c t)})

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