JEE Main 2021 — Differential Equations Question with Solution
From: JEE Main 2021 (Online) 18th March Evening Shift
Question
Let y = y(x) be the solution of the differential equation
xdy ydx = , x 1, with y(1) = 0. If the area bounded by the line x = 1, x = e, y = 0 and y = y(x) is e2 + , then the value of 10( + ) is equal to __________.
xdy ydx = , x 1, with y(1) = 0. If the area bounded by the line x = 1, x = e, y = 0 and y = y(x) is e2 + , then the value of 10( + ) is equal to __________.
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Show full solutionCorrect answer: 4
Correct answer
4
Step-by-step explanation
dividing both sides by x2, we get
Integrating both side, we get
Given, y(1) = 0 at x = 1, y = 0
C = 0
y = x sin(ln(x))
Area
Let, lnx = t
x = et
dx = et dt
New lower limit, t = ln(1) = 0
and upper limit t = ln =
Area =
So,
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This is a previous-year question from JEE Main 2021, 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.