Let the solution curve x=x(y), 0< y< \frac{\pi}{2}, of the differential equation (\log _e(\cos y)) ^2 \cos y \dx- (1+3 x \log _e. (cos y)) \sin y d y=0 satisfy x (\frac{\pi}{3}) = {1}/{2 \log _{ {\c}} 2}. If x (\frac{\pi}{6}) = {1}/{\log _{ {\e}} m-\log _{ {\c}} n}, where m and n are co-prime, then m n is equal to [8-Apr-2023 shift 2]

JEE Mains 8-Apr-2023 Shift 2 Solved Paper

Section: Mathematics

Question : 27 of 90

Marks: +1, -0

Let the solution curve x=x(y),0<y<‌

, of the differential equation (loge(cos‌y))2‌cos‌y‌dx−(1+3xloge. (cos y))‌s‌i‌n‌ydy=0 satisfy x(‌

)=‌

2logc2

. If x(‌

)=‌

logem−logcn

, where m and n are co-prime, then mn is equal to

[8-Apr-2023 shift 2]

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