derv quest?

Question

(y/x)+(x/y)=2y

find this derv

Answer 1

(xy' -y)/x^2 +(y-xy')y^2 =2y'
y^2(xy'-y)+ x^2(y- xy')= 2x^2y^2y'
xy^2y'- y^3 +x^2y -x^3y' = 2x^2y^2y'
xy^2y'-x^3y'-2x^2y^2y' = y^3 +x^2y
y'(xy^2 -x^3 -2x^2y^2) = y^3+x^2y
y' = [y(x^2+y^2)]/[x(y^2-x^2 -2xy^2)]

Answer 2

[xdy/dx-y]+[y-xdy/dx]=2dy/dx