JEE Main 2019MathematicsDifferential EquationsMediumMCQ

JEE Main 2019 — Differential Equations Question with Solution

JEE Main 2019 (10 Jan Shift 2)

Question

A curve amongst the family of curves represented by the differential equation, x2-y2 dx+2xy dy=0 which passes through 1,1, is

Choose an option

Show full solutionCorrect option: A
Correct answer
AA circle with centre on the x- axis.

Step-by-step explanation

x2dx-y2dx+2xy dy=0

x2dx=y2dx-2x ydy

⇒-dx=dy2x  (exact differential equation)

⇒ -x=y2x+C

⇒ x2+y2+Cx=0

∵ It passes through 1,1.

Hence, C=-2

⇒ x2+y2-2x=0

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About this question

This is a previous-year question from JEE Main 2019, 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.