Obtain the differential equation of the curve `y=a_(1) e^(x) + a_2 e^(-x) where , a_1 , a_2`being arbitrary constant.

The differential equation of the family of curves y=e^(x)(A cos x+B sin x), where A and B are arbitrary constants is

The differential equation of the family y = ae^(x) + bx e^(x) + cx^(2)e^(x) of curves where, a,b,c are arbitrary constants is

Find the differential equation representing the family of curves y=a.e^(2x)+5 , where a is an arbitrary constant.

The differential equation of the family of curves y=e^(2x)(a cos x+b sin x) where, a and b are arbitrary constants, is given by

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.

The differential equaiotn which represents the family of curves y=C_(1)e^(C_(2)x) , where C_(1) and C_(2) are arbitrary constants, is

Obtain the differential equation by eliminating the arbitrary constants from the following equation : y = c_(1) e^(2 x) + c_(2) e^(-2x).