Form a differential equation representing the given family of curves `y=Ae^(2x)+Be^(-2x)`

From a differential equation representing the given family of curves by eliminating the arbitrary constains a and b x/a + y/b = 1

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

From the differential equation representing the family of curves y=asin(x+b) ,where a and b are arbitrary constants.

Form the differential equation representing the family of curve given by (x-a)^2+2y^2=a^2 ,a is a arbitrary constants.

The differential equation representing the family of curves y=xe^(cx) (c is a constant ) is a) (dy)/(dx)=(y)/(x)(1-"log"(y)/(x)) b) (dy)/(dx)=(y)/(x)"log"((y)/(x))+1 c) (dy)/(dx)=(y)/(x)(1+"log"(y)/(x)) d) (dy)/(dx)+1=(y)/(x)"log"((y)/(x))

The differential equation representing the family of curves y^(2) = a(ax + b) , where a and b are arbitrary constants, is of

The differential equation representing the family of curves given by y=ae^(-3x)+b , where a and b are arbitrary constants, is a) (d^(2)y)/(dx^(2))+3(dy)/(dx)-2y=0 b) (d^(2)y)/(dx^(2))-3(dy)/(dx)=0 c) (d^(2)y)/(dx^(2))-3(dy)/(dx)-2y=0 d) (d^(2)y)/(dx^(2))+3(dy)/(dx)=0

The differential equation representing the family of curves y^(2) = 2c (x + sqrt(c)) , where c is a positive parameter, is of a)order 1, degree 2 b)order 1, degree 3 c)order 2, degree 3 d)order 2, degree 2

Find the Differential equation satisfying the family of curves y=ae^(3x)+be^(-2x) ,a and b are arbitrary constants.