JEE Main 2021MathematicsDifferentiationHardNumerical

JEE Main 2021 — Differentiation Question with Solution

JEE Main 2021 (27 Aug Shift 1)

Question

If y1/4+y-1/4=2x, and x2-1d2ydx2+αxdy dx+βy=0, then |α-β| is equal to _______.

Enter your answer

Show full solutionCorrect answer: 17
Correct answer
17

Step-by-step explanation

y14+1y14=2x

y142-2xy14+1=0

y14=x+x2-1& x-x2-1

So, 141y34 dydx=1+xx2-1

141y34dydx=y14x2-1

dydx=4yx2-1   ...1

Hence 

d2ydx2=4x2-1y'-xyx2-1x2-1

x2-1y"=4x2-1y'-xyx2-1

x2-1y'=4x2-1y'-xyx2-1

x2-1y"=44y-xy'4  1

x2-1y"+xy'-16y=0

So  α-β=17

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Differentiation chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

About this question

This is a previous-year question from JEE Main 2021, 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.