If (x^2+y^2) ,dy=xy ,dx, with y(x_0)=e, y(1)=1, then x_0 has the value

MHT CET 2022 Mathematics question

If , with , , then has the value

Answer: (A)

The equation is homogeneous: put , . Then , so and . Integrate: , i.e. , which is

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Question ID VK-094324