JEE Main 2021 · Mathematics · Differential Equations · hard

The solution of dy/dx+ytan x=sec x with y(0)=2 gives y ((π)/(4))=

Single correct option

The solution of

\dfrac{dy}{dx}+y\tan x=\sec x

with

y(0)=2

gives

y\!\left(\dfrac{\pi}{4}\right)=

Show answer and solution

Answer: (A) $\dfrac{3}{\sqrt2}$

The integrating factor is

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

. Then

\dfrac{d}{dx}(y\sec x)=\sec^2x

, so

y\sec x=\tan x+C

, i.e.

y=\sin x+C\cos x

. From

y(0)=2

we get

C=2

. Therefore

y(\pi/4)=\dfrac{1}{\sqrt2}+\dfrac{2}{\sqrt2}=\dfrac{3}{\sqrt2}

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