JEE Main 2022MathematicsDifferentiationMediumMCQ

JEE Main 2022 — Differentiation Question with Solution

JEE Main 2022 (27 Jun Shift 1)

Question

If cos-1y2=logex55,y<2, then

Choose an option

Show full solutionCorrect option: D
Correct answer
Dx2y''+xy'+25y=0

Step-by-step explanation

Given,

cos-1y2=logex55

Using property logxm=mlogx we get,

cos-1y2=5logex5

Now differentiating both side w.r.t x we get,

-11-y24·y'2=5·1x5·15

⇒-y'4-y2=5x

⇒-xy'=54-y2

Again differentiating w.r.t x we get,

⇒-xy''-y'=5·124-y2-2yy'

⇒xy''+y'=5yy'4-y2

⇒xy''+y'=5y·-5x

⇒x2y''+xy'=-25y

⇒x2y''+xy'+25y=0

 

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About this question

This is a previous-year question from JEE Main 2022, covering the Differentiation 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.