1.

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»


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.


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