Verified Solution • 2025–26 Session moderate

QJEEM21Ma80d6: JEE Main 2021 Mathematics - Class 12 JEEM21Ma80d6 Solution: If is the solution of the differential equation , with y(0) =…

If y=y(x),y∈[0,π2)y = y(x),y \in \left[ {0,{\pi \over 2}} \right) is the solution of the differential equation sec⁡ydydx−sin⁡(x+y)−sin⁡(x−y)=0\sec y{{dy} \over {dx}} - \sin (x + y) - \sin (x - y) = 0 , with y(0) = 0, then 5y′(π2)5y'\left( {{\pi \over 2}} \right) is equal to ______________.

Step-by-Step Verified Solution

sec⁡ydydx=2sin⁡xcos⁡y\sec y{{dy} \over {dx}} = 2\sin x\cos y

sec⁡2ydy=2sin⁡xdx{\sec ^2}ydy = 2\sin xdx

tan⁡y=−2cos⁡x+c\tan y = - 2\cos x + c

c=2c = 2

tan⁡y=−2cos⁡x+2⇒\tan y = - 2\cos x + 2 \Rightarrow at x=π2x = {\pi \over 2}

tan⁡y=2\tan y = 2

sec⁡2ydydx=2sin⁡x{\sec ^2}y{{dy} \over {dx}} = 2\sin x

∴\therefore 5dydx=25{{dy} \over {dx}} = 2

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