The differential equation for the family of curves  x2−y2−2ay=0 where a is an arbitrary constant, is

We have,x2+y2−2ay=0Differentiating w.r. to x, we get2x+2ydydx−2adydx=0⇒a=x+ydydxdydxSubstituting this value of a in (i), we getx2+y2dydx−2yx+ydydx=0⇒x2−y2dydx=2xyThis is the required differential equation.