JEE Main 2016MathematicsDifferential EquationsSolution Of Differential Equations By Method Of Separation Variables And HomogeneousmediumMCQ

JEE Main 2016Differential Equations Question with Solution

From: JEE Main 2016 (Online) 9th April Morning Slot

Question

If   f(x) is a differentiable function in the interval (0, ) such that f (1) = 1 and

  for each x > 0, then equal to :

Choose an option

Show full solutionCorrect option: D
Correct answer
D

Step-by-step explanation



It is in form

So, applying L' Hospital rule,



   2xf(x) x2f '(x) = 1

   f '(x) f(x)

   I.F =

   Solution of equation,

f(x) =

   

Given that,

f(1) = 1

    = + C

   C

   f(x) x2 +

   f

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Differential Equations 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 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.