Find the differential equation corresponding to `y=a e^(2x)+b e^(-3x)+c e^x` where `a ,\ b ,\ c` are arbitrary constants.

Find the differential equation corresponding to jy=ae^(2x)+be^(-3x)+ce^(x) where a,b,c are arbitrary constants.

Find the differential equation corresponding to the equation y=A*e^(x)+B .

Find the differential equation conistent with y=ae^(3x)+be^(5x)+ce^(7x) , where a,b,c are arbitrary constants.

Find the differential equation corresponding to curve y=A sin x+Bcos x+x sin x , where A and B are arbitrary constants.

Form the differential equation corresponding to y^(2)=a(b-x)^(2), where a and b are arbitrary constant.

Find the order of the differential equation corresponding to (i) y = c(x-c)^(2) where c is an arbitrary constant. (ii) y = Ae^(x) + Be^(3x) + Ce^(5x) where A, B, C are arbitrary constant. (iii) xy = c e^(x) + b e^(-x) + x^(2) where b, c are arbitrary constants. (iv) The family of all circles in the xy-plane with centre at the origin.

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.

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