JEE Main 2016 — Differential 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 :
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
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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.