The solution of the differential equation dy dx + y2 x = x 2y , where 0 x < 2 and y(0) = 1, is given by

JEE Main 2016 Mathematics question

The solution of the differential equation , where and , is given by

Answer: (4)

Multiply through by to turn the equation into one that is linear in :

2y + x = x.

Substituting , so that , gives

+ v x = x.

The integrating factor is , and

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Question ID VK-115669