Let y'(x) + y(x)g'(x) = g(x)g'(x), y(0) = 0, x R , where f'(x) denotes d f(x) dx and g(x) is a given non-constant differentiable function on R with g(0) = g(2) = 0. Then the value of y(2) is

JEE Advanced 2011 Mathematics question

Let , , , where f'(x) denotes and g(x) is a given non-constant differentiable function on with . Then the value of y(2) is

Answer: 0

This is a linear differential equation with integrating factor : . Integrating (substitute ): $

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Question ID VK-025998