The differential equation representing the family of curves y^2 = 2c(x + c ), where c is a positive parameter, is of

MHT CET 2023 Mathematics question

The differential equation representing the family of curves , where c is a positive parameter, is of

(A)order 1, degree 4
(B)order 2, degree 3
(C)order 2, degree 4
(D)order 1, degree 3Correct

Answer: (D)

Solution

Differentiate once: , so . Substitute in the family: , i.e. . Squaring to remove the radical: . Only one derivative appears (highest derivative is of order 1, and one arbitrary constant was

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Question ID VK-098231