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