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Question Id : 13331 | Context : JEE Main 2023 (1 February Evening Shift)
Let $\alpha x = \exp(x^{\beta} y^{\gamma})$ be the solution of the differential equation $2x^{2}y\,dy - (1 - xy^{2})\,dx = 0,\ x>0,\ y(2)=\sqrt{\log_{e}2}.$ Then $\alpha + \beta - \gamma$ equals:


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