x^2 +y^2 =2ay    here a=constant  .. use the substitution of y=tx      from this find the integration of  dx/y

 diff. whole eqn w.r.t  x

we get, 2x+(2y) y'= 2ay'

now put value "a" frm given eqn in it { a=(x²+y²)/2y  }

u will get diff eqn in x, y and y'

ie. (x²-y²)y'= 2xy