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Differential Equations question

2023 · 8 Apr · Shift 2 · Q40

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JEE Main
Mathematics
Differential Equations
2023 · 8 Apr · Shift 2 · Q40

Differential Equations question

2023 · 8 Apr · Shift 2 · Q40

JEE MainMathematicsDifferential EquationsNumerical+4 / −1

Let the solution curve

x=x(y), 0 \lt y \lt \frac{\pi}{2}

, of the differential equation

\left(\log _{e}(\cos y)\right)^{2} \cos y \mathrm{~d} x-\left(1+3 x \log _{e}(\cos y)\right) \sin \mathrm{y} d y=0

satisfy

x\left(\frac{\pi}{3}\right)=\frac{1}{2 \log _{e} 2}

. If

x\left(\frac{\pi}{6}\right)=\frac{1}{\log _{e} m-\log _{e} n}

, where

m

and

n

are coprime, then

m n

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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