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Differential Equations question

2024 · 8 Apr · Shift 2 · Q57

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JEE Main
Mathematics
Differential Equations
2024 · 8 Apr · Shift 2 · Q57

Differential Equations question

2024 · 8 Apr · Shift 2 · Q57

JEE MainMathematicsDifferential EquationsNumerical+4 / −1

Let

\alpha|x|=|y| \mathrm{e}^{x y-\beta}, \alpha, \beta \in \mathbf{N}

be the solution of the differential equation

x \mathrm{~d} y-y \mathrm{~d} x+x y(x \mathrm{~d} y+y \mathrm{~d} x)=0,y(1)=2

. Then

\alpha+\beta

is equal to

\underline{\hspace{2cm}}

Numerical answer

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