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Differential Equations question

2023 · 1 Feb · Shift 2 · Q39

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JEE Main
Mathematics
Differential Equations
2023 · 1 Feb · Shift 2 · Q39

Differential Equations question

2023 · 1 Feb · Shift 2 · Q39

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

Let

\alpha x=\exp \left(x^{\beta} y^{\gamma}\right)

be the solution of the differential equation

2 x^{2} y \mathrm{~d} y-\left(1-x y^{2}\right) \mathrm{d} x=0, x \gt 0,y(2)=\sqrt{\log _{e} 2}

. Then

\alpha+\beta-\gamma

equals :

A
1
B
0
C
3
D
$-1$

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