Let $\alpha x=\exp \left(x^\beta y^\gamma\right)$ be the solution of the differential equation $2 x^2 y d y-\left(1-x y^2\right) d x=0, x0, y(2)=\sqrt{\log _e 2}$. Then $\alpha+\beta-\gamma$ equals: [JEE Main 2023, 1 Feb (Shift 2)]

Question

Let $\alpha x=\exp \left(x^\beta y^\gamma\right)$ be the solution of the differential equation $2 x^2 y d y-\left(1-x y^2\right) d x=0, x>0, y(2)=\sqrt{\log _e 2}$. Then $\alpha+\beta-\gamma$ equals: [JEE Main 2023, 1 Feb (Shift 2)]

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Let \(\alpha x=\exp \left(x^\beta y^\gamma\right)\) be the solution of the differential equation \(2 x^2 y d y-\left(1-x…

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