The differential equation whose solution represents the family x^2y = 4e^x + c, where c is an arbitrary constant, is

MHT CET 2025 Mathematics question

The differential equation whose solution represents the family , where c is an arbitrary constant, is

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

Answer: (D)

Solution

Taken literally, differentiating gives , which contains and matches none of the options, so the intended family is (the constant multiplying , the usual way an arbitrary constant is eliminated in such options). Differentiate: x^2$ =

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Question ID VK-101404