Differentiate the equation y+ xy = 2x+y^2 and find dy/dx

Given the equation:

y + xy =
2x + y^2

We will use implicit differentiation to find
dy/dx

We will differentiate with respect to
x.

==> y' + ( x'*y + x*y') = 2 +
2yy'

==> y' + y + xy' = 2+
2yy'

Now we will group all terms with y' on one
side.

==> y' + xy' -2yy' = 2
-y

Now we will factor
y'.

==> y'(1 + x -2y) =
(2-y)

Now we will divide by
(1+x-2y)

==> y' =
(2-y)/(1+x-2y)

Then the values of dy/dx =
(2-y)/(1+x-2y)