JEE Main 2016MathematicsDifferential EquationsMediumMCQ

JEE Main 2016 — Differential Equations Question with Solution

JEE Main 2016 (10 Apr Online)

Question

The solution of the differential equation dydx+y2sec⁡x=tan⁡x2y, where 0≤x<π2 and y0=1, is given by

Choose an option

Show full solutionCorrect option: D
Correct answer
Dy2=1-xsec⁡x+tan⁡x

Step-by-step explanation

dydx+y2sec⁡x=tan⁡x2y
2ydydx+y2sec⁡x=tan⁡x
Put y2=t ⇒2ydydx=dtdx
dtdx+tsec⁡x=tan⁡x
 I.F=e∫sec⁡xdx=eln(sec⁡x+tanx)=sec⁡x+tan⁡x
⇒tsec⁡x+tan⁡x=∫sec⁡x+tan⁡xtan⁡xdx
⇒tsec⁡x+tan⁡x=∫sec⁡xtan⁡xdx+∫tan2⁡xdx
⇒y2sec⁡x+tan⁡x=sec⁡x+tan⁡x-x+c
y0=1 ⇒c=0
⇒y2=1-xsec⁡x+tan⁡x

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About this question

This is a previous-year question from JEE Main 2016, 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.