Let y(x) be the solution of the differential equation x^2 dy dx + xy = x^2 + y^2, x > 1 e , satisfying y(1) = 0. Then the value of 2 (y(e))^2 y(e^2) is _____.

JEE Advanced 2025 Mathematics question

Let y(x) be the solution of the differential equation

+ xy = + , x > ,

satisfying y(1) = 0. Then the value of is .

Answer: 0.75

Put y = vx: . y(1) = 0 gives v = 0 at x = 1, so C = 1 and

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Question ID VK-035474