Let f(x) be differentiable on the interval (0, ∞) such that f(1) = 1, and _ t x t^2f(x) - x^2f(t) t - x = 1 for each x > 0. Then f(x) is

JEE Advanced 2007 Mathematics question

Let f(x) be differentiable on the interval (0, ∞) such that f(1) = 1, and

= 1

for each x > 0. Then f(x) is

Answer: (A)

The limit is a 0/0 form; by L'Hôpital's rule with respect to t: . So . Integrating factor :

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Question ID VK-037449