Solve for dy/dx .

x^2+y^2=2xy

x^{2}+y^{2}=2xy

2x+2y dy/dx = 2y+2x dy/dx

dy/dx (2y-2x) =2y-2x

dy/dx = (2y-2x)/(2y-2x) =1 if y is not equal to y

Alternatively

(x-y)^{2} =0

2(x-y)(1-dy/dx) =0

If x not equal to y dy/dx =1

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