arrange
xdx+ylnxdx-xlnxdy=0
Divide by x at the same time? lnx
get
1/(xlnx)dx+(ydx-xdx)/x? =0
That is, d(ln(lnx))+d(-y/x)=0.
So the original equation is ln (lnx)-y/x = c.
Substituting into a fixed point gives c =-1/e.
So the original function is
y=xln(lnx)+x/e