Use variation of parameters followed by separation of variables to solve the following differential equation. Use lower c\displaystyle {c} for the constant of integration

y′+y=2xe−x1+yex\displaystyle {y}'+{y}=\frac{{{2}{x}{e}^{{-{x}}}}}{{{1}+{y}{e}^{{x}}}}



(A) Solution with positive square root coefficient
y(x)=\displaystyle {y}{\left({x}\right)}=  



(B) Solution with negative square root coefficient
y(x)=\displaystyle {y}{\left({x}\right)}=  

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