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Given the equation:

2xy + x^2 = 3y + y^2

We need to find y' or dy/dx

We will use implicit differentiation to find y'

==> Let us apply the differentiation for all terms.

==> (2xy)' + (x^2)' = (3y)' + (y^2)'

==> (2x)'*y + (2x)*y' + 2x = 3y' + 2yy'

==> 2y + 2xy' +2x = 3y' + 2yy'

Now we will combine all terms with y' on the left side.

==> 2xy' - 3y' - 2yy' = -2x-2y

Now we will factor y' from the left side.

==> y'*(2x -3 -2y) = -2(x+y)

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

==> y' = -2(x+y)/(2x-2y-3)

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