JEE Main 2020MathematicsDifferential EquationsMediumMCQ

JEE Main 2020 — Differential Equations Question with Solution

JEE Main 2020 (02 Sep Shift 1)

Question

Let y=yx be the solution of the differential equation, 2+sinxy+1.dydx=−cosx, y>0, y0=1. If yπ=a and dydx at x=π is b, then the ordered pair a, b is equal to

Choose an option

Show full solutionCorrect option: C
Correct answer
C1, 1

Step-by-step explanation

dy1+y=-cosx2+sinxdx

ln1+y=-ln2+sinx+lnc

1+y2+sinx=c

We know y0=1

Soc=4

1+y=42+sinx  ⇒  y=42+sinx-1

yπ=2-1=1=a

dydx=-42+sinx2·cosx=1

At  x=π⇒b=1

a,b=1,1

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About this question

This is a previous-year question from JEE Main 2020, covering the Differential Equations chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.