Q.Let $x = x(y)$ be the solution of the differential equation $y^{2} dx + (x - 1/y) dy = 0.$ If $x(1) = 1,$ then $x(1/2)$ is:

1/2 + e

3/2 + e

3 - e

3 + e

The correct solution involves applying the fundamental concept to derive the final value step by step...

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Q.Let x=x(y)x = x(y)x=x(y) be the solution of the differential equation y2dx+(x−1/y)dy=0.y^{2} dx + (x - 1/y) dy = 0.y2dx+(x−1/y)dy=0. If x(1)=1,x(1) = 1,x(1)=1, then x(1/2)x(1/2)x(1/2) is: