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Differential Equations question

2024 · 29 Jan · Shift 1 · Q60

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JEE Main
Mathematics
Differential Equations
2024 · 29 Jan · Shift 1 · Q60

Differential Equations question

2024 · 29 Jan · Shift 1 · Q60

JEE MainMathematicsDifferential EquationsNumerical+4 / −1

If the solution curve

y=y(x)

of the differential equation

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

passes through the point

(1,1)

and

y(e)=\frac{\alpha-\tan \left(\frac{3}{2}\right)}{\beta+\tan \left(\frac{3}{2}\right)}

, then

\alpha+2 \beta

is

\underline{\hspace{2cm}}

.

Numerical answer

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