JEE Main 2024MathematicsDifferential EquationsMediumMCQ

JEE Main 2024 — Differential Equations Question with Solution

JEE Main 2024 (31 Jan Shift 1)

Question

The solution curve of the differential equation ydxdy=xlogex-logey+1, x>0, y>0 passing through the point (e, 1) is

Choose an option

Show full solutionCorrect option: C
Correct answer
Clogexy=y

Step-by-step explanation

Given: ydxdy=xlogex-logey+1, x>0, y>0

⇒dxdy=xylogexy+1

Putting, x=vy

⇒dxdy=v+ydvdx

⇒v+ydvdy=vyylogevyy+1

⇒v+ydvdy=vlogev+1

⇒v+ydvdy=vlogev+v

⇒ydvdy=vlogev

⇒dvvlogev=dyy

⇒∫dvvlogev=∫dyy

Putting, logev=t

⇒dvv=dt

⇒∫dtt=∫dyy

⇒logt=logy+c

⇒loglogexy=logy+c

Using point e,1

⇒loglogee=log1+c

⇒c=0

⇒loglogexy=logy

⇒logexy=y

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About this question

This is a previous-year question from JEE Main 2024, 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.