The differential equation whose solution is Ax^2+By^2=1 where A and B are arbitrary constants is of

MHT CET 2025 Mathematics question

The differential equation whose solution is where A and B are arbitrary constants is of

(A)degree 1 and order 2Correct
(B)degree 2 and order 1
(C)degree 3 and order 2
(D)degree 1 and order 3

Answer: (A)

Solution

The family has two arbitrary constants and , so the differential equation has order 2. Differentiate: 2Ax+2By\,y'=0\Rightarrow Ax+By\,y'=0. Differentiate again: . Eliminating (from the first, ):

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Question ID VK-102428