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.

Form the differential equation of the family of curves represented by y^2=(x-c)^3 .

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

Form a differential equation of the family of the curves y^(2)=4ax

Form a differential equation of the family of the curves y^2 =4ax .

The differential equation of the family of curves represented by y^3= cx+ c^3+ c^2-1 ,where c is an arbitrary constant is of :

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

Find the differential equation of the family of curves y=A e^(2x)+B e^(-2x) , where A and B are arbitrary constants.

Find the differential equation of the family of curves y=A e^(2x)+B e^(-2x) , where A and B are arbitrary constants.

Find the differential equation of the family of curves y=A e^(2x)+B e^(-2x) , where A and B are arbitrary constants.