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Differential Equations question

2023 · 13 Apr · Shift 2 · Q41

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JEE Main
Mathematics
Differential Equations
2023 · 13 Apr · Shift 2 · Q41

Differential Equations question

2023 · 13 Apr · Shift 2 · Q41

JEE MainMathematicsDifferential EquationsNumerical+4 / −1

If

y=y(x)

is the solution of the differential equation

\frac{d y}{d x}+\frac{4 x}{\left(x^{2}-1\right)} y=\frac{x+2}{\left(x^{2}-1\right)^{\frac{5}{2}}}, x \gt 1

such that

y(2)=\frac{2}{9} \log _{e}(2+\sqrt{3}) \text { and } y(\sqrt{2})=\alpha \log _{e}(\sqrt{\alpha}+\beta)+\beta-\sqrt{\gamma}, \alpha, \beta, \gamma \in \mathbb{N} \text {, then } \alpha \beta \gamma \text { is equal to }

:

Numerical answer

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