QJEEM21Ma0f38: JEE Main 2021 Mathematics - Class 12 JEEM21Ma0f38 Solution: If y = y(x) is the solution of the differential equation + (tan …

Question

Verified Solution • 2025–26 Session moderate

If y = y(x) is the solution of the differential equation

{{dy} \over {dx}}

+ (tan x) y = sin x,

0 \le x \le {\pi \over 3}

, with y(0) = 0, then

y\left( {{\pi \over 4}} \right)

equal to :

Accepted Answer

Integrating Factor

= {e^{\int {\tan x\,dx} }} = {e^{\ln (\sec x)}} = \sec x

y\sec x = \int {(\sin x)\sec x\,dx = \ln (\sec x) + C}

y(0) = 0 \Rightarrow C = 0

\therefore

y = \cos x\ln |\sec x|

y\left( {{\pi \over 4}} \right) = {1 \over {\sqrt 2 }}\ln \left( {\sqrt 2 } \right) = {1 \over {2\sqrt 2 }}\ln 2

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