Please, help me to solve this problem. I don't know how to deal with (x) near dy and dx...
One more step just for fun:
$\displaystyle \frac{1}{e}\left(e^y(y-1)\right)=(ln(x)+c)\frac{1}{e}$
$\displaystyle (y-1)e^{y-1}=\frac{1}{e}(ln(x)+c)$
Taking the Lambert-W function of both sides:
$\displaystyle y-1=\textbf{W}\left[\frac{1}{e}(ln(x)+c)\right]$
or:
$\displaystyle y(x)=1+\textbf{W}\left[\frac{1}{e}(ln(x)+c)\right]$