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.

Answer

(i) Since there is only one arbitrary constant, the order is 1
(ii) since there are 3 independent arbitrary constants order 3.
(iii) Since there are 2 independent arbitrary constants order 2.
(iv) `x^(2) + y^(2) = a^(2)`, a is a parameter has only one arbitrary constant, order 1.