Let y = y(x) be the solution curve of the differential equation dy/dx + ((2x^ 2 + 11x + 13)/(x^ 3 + 6x^ 2 + 11x + 6))y = (x + 3)/(x + 1), x < −1, which passes through the point (0, 1). Then y(1) is equal to:

JEE Main 2022 Mathematics question

Let y = y(x) be the solution curve of the differential equation dy/dx + ( + 3)/(x + 1), x < −1, which passes through the point (0, 1). Then y(1) is equal to:

(1)1/2
(2)3/2Correct
(3)5/2
(4)7/2

Answer: (2)

Solution

Since , partial fractions give ( + 13)/((x + 1)(x + 2)(x + 3)) = 2/(x + 1) + 1/(x + 2) − 1/(x + 3). The integrating factor is ( + 2)/(x + 3). So

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Question ID VK-035055