Separating variables:

`{:(x\ dy=y\ ln\ y\ dx),((dy)/(y\ ln\ y)=(dx)/x):}`

Integrating: [For the y part, let u = ln y, then du = dy/y].

`{:(int(dy)/(y\ ln\ y)=int(dx)/x),(ln(ln\ y)=ln\ x+K):}`

Substituting x = 2 when y = e gives:

`{:(ln(ln\ e)=ln\ 2+K),(ln(1)=ln\ 2+K),(0=ln\ 2+K),(K=-ln\ 2):}`

Substituting this in our general solution:

`ln(ln\ y)=ln\ x-ln\ 2` `=ln\ x/2`

This gives us:

`ln\ y=x/2`

So the particular solution is given by:

`y=e^(x//2)`