" ii) "(x-y log y+y log x)dx+x(log y-log x)dy=0

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Solve : (x-y log y+y log x)dx+x(logy-logx)dy=0

y log y dx - x dy = 0

Solve y log y dx + (x-log y) dy = 0.

y log y (dx)/(dy) + x - log y =0

If y = log log (log x), then dy/dx =

solve x((dy)/(dx))=y(log y-log x+1)

(x log x ) (dy)/(dx) + y = 2 log x