Let the solution curve y = y(x) of the differential equation [x/ x^ 2 - y^ 2 + e^ y /^ x ] x dy/dx = x + [x/ x^ 2 - y^ 2 + e^ y /^ x ]y pass through the points (1, 0) and (2 , ), > 0. Then is equal to

JEE Main 2022 Mathematics question

Let the solution curve y = y(x) of the differential equation x dy/dx = pass through the points (1, 0) and (, ), . Then is equal to

Answer: (1)

Dividing by x, [ + /dx) = + /x). Put y = tx: dt/dx) = , so . Integrating, $

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Question ID VK-034965