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JEE Main 20206 SeptemberEvening Shift
Exam
JEE Main
Year
2020
Date
6 September
Shift
Evening Shift
Subject
Mathematics
Chapter
Differential Equations

JEE Main 2020 · 6 September · Evening Shift · Mathematics · Differential Equations

If y = ((2)/(π)x - 1)cosecx is the solution of the differential...

If y=(2πx−1)cosecxisthesolutionofthedifferentialequation,y = \left(\dfrac{2}{\pi}x - 1\right)cosecx is the solution of the differential equation,\dfrac{dy}{dx} + p\left(x\right)y = - \dfrac{2}{\pi}cosecx, 0 < x < \dfrac{\pi}{2},thenthefunction, then the functionp\left(x\right) is equal to :

Options

  1. Acot⁡x\cot x
  2. Bcosecxcosecx
  3. Csec⁡x\sec x
  4. Dtan⁡x\tan x

Correct answer

A. cot⁡x\cot x

Step-by-step solution

y=(2πx−1)cosecxy = \left(\dfrac{2}{\pi}x - 1\right)cosecx

⇒dydx=2πcosecx−(2xπ−1)cosecxcotx⇒ \dfrac{dy}{dx} = \dfrac{2}{\pi}cosecx - \left(\dfrac{2x}{\pi} - 1\right)cosecxcotx cotxcot x

⇒dydx+(2xπ−1)cosecxcotx=2πcosecx⇒ \dfrac{dy}{dx} + \left(\dfrac{2x}{\pi} - 1\right)cosecxcotx = \dfrac{2}{\pi}cosecx

⇒dydx+ycotx=2πcosecx⇒ \dfrac{dy}{dx} + ycotx = \dfrac{2}{\pi}cosecx

⇒p(x)=cot⁡x⇒ p\left(x\right) = \cot x

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