Here,
2x2

dx

dy

- 2xy + y2 = 0

dy

dx

=

2xy−y2

2x2

Hence the given equation is an homogeneous equation.
Let y = vx
and

dy

dx

= y + x

dv

dx

So, v + x

dv

dx

So, v + x

dv

dx

=

2x(vx)−(vx)2

2x2

=

2v−v2

2

= v−

v2

2

⇒ x

dv

dx

= -

v2

2

⇒ 2 ∫

1

v2

dv = ∫ −∫

dx

x

⇒ 2 (−

1

v

) = - log |x| + c
⇒

2x

y

= log |x| + c