Obtain the differential equation of the family of circles `x^2 + y^2+2gx + 2fy + c = 0` ; where `g ,f& c` are arbitrary constants.

Find the differential equation of the family of circles (x-a)^(2)+(y-b)^(2)=r^(2) , where 'a' and 'b' are arbitrary constants.

From the differential equation of the family of circles (x -a)^(2) + (y - a)^(2) - a^(2) , where a is an arbitrary constant .

Obtain the differential equation of the family of curves represented by y=Ae^x+Be^-x+x^2 , where A and B are arbitrary constants.

Obtain the differential equation of the family of curves represented by y=Ae^x+Be^-x+x^2 , where A and B are arbitrary constants.

Form the differential equation representing the family of curves given by (x - a)^2 + 2y^2 = a^2 , where a is an arbitrary constant.

The differential equation of family of curves x^(2) + y^(2) - 2ay = 0 where 'a' is arbitrary constant is

Form the differential equation representing the family of curves given by (x-a)^2 + 2y^2 = a^2 , where a is an arbitrary constant.