The differential equation, having general solution as Ax^ 2 +By^ 2 =1, where A and B are arbitrary constants, is

MHT CET 2024 Mathematics question

The differential equation, having general solution as , where and are arbitrary constants, is

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

Answer: (D)

Solution

Two arbitrary constants, so differentiate twice and eliminate . First: 2Ax+2By\,y'=0\Rightarrow Ax+By\,y'=0. Second: . From the first, ; substitute in the second:

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Question ID VK-098963