Let y = y(x), x > 1, be the solution of the differential equation (x − 1)dy/dx + 2xy = 1/(x − 1), with y(2) = (1 + e^ 4 )/(2e^ 4 ). If y(3) = (e^ + 1)/( e^ ), then the value of + is equal to _____.

JEE Main 2022 Mathematics question

Let y = y(x), x > 1, be the solution of the differential equation (x − 1)dy/dx + 2xy = 1/(x − 1), with . If , then the value of is equal to .

Answer: 14

Dividing by (x − 1): dy/dx + (2x/(x − 1))y = 1/(x − . The integrating factor is dx/(x − 1)} = + 2/(x − 1))dx} = = − . Then d(y − ) = , so y −

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Question ID VK-035247