The solution of the differential equation dy dx = a+bx c+dy represents a family of circles centered at the origin if …

MHT CET 2026 Mathematics question

The solution of the differential equation represents a family of circles centered at the origin if …

(A)Correct
(B)
(C)
(D)

Answer: (A)

Solution

Separate variables: (c+dy)\,dy=(a+bx)\,dx. Integrate: , i.e. . A circle centred at the origin has the form : no or term, so and , and the coefficients of and must be equal, so , i.e.

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Question ID VK-101100