Question 1184043
You said your answer was 

{{{ x + y + xy - 2ln(xy) = c}}}, for constant c.

If you apply implicit differentiation on this equation, you will get


{{{1 + dy/dx + (1*y + x*(dy/dx)) - 2*(1/(xy))*(1*y + x*(dy/dx))  = 0}}}


<===> {{{1 + dy/dx + y + x*(dy/dx) - 2/x - (2/y)*(dy/dx)  = 0}}}

<===> {{{1 + (1+x - 2/y)(dy/dx) + y - 2/x  = 0}}}

<===>  {{{(1+x - 2/y)(dy/dx) + y   = 2/x - 1}}}, which is exactly the given D.E.


Better ask your instructor as to what particular detail you messed up at.