Form a differential equation for the family of curves represented by `ax^2 + by^2 = 1`, 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.

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.

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

Form the differential equation of the family of curves represented by y = a cos (bx + c) where a, b, c are the arbitrary constants.

From the differential equation of the family of curves represented by y = a cos (bx + c) where a, b, c are the arbitrary constants.

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

The differential equation of the family of curves represented by y = a + bx + ce^-x (where a, b, c are arbitrary constants) is

Form the differential equation representi.ng the family of curves y = a sin (x + b) , where a and b are arbitrary constants

From the differential equation for the family of the curves y^(2)=a(b^(2)-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.