JEE Main 2016MathematicsDifferential EquationsMediumMCQ

JEE Main 2016 — Differential Equations Question with Solution

JEE Main 2016 (03 Apr)

Question

If a curve y=fx passes through the point (1,-1) and satisfies the differential equation, y 1+xydx=x dy, then f-12 is equal to

Choose an option

Show full solutionCorrect option: B
Correct answer
B45

Step-by-step explanation

Given differential equation,

ydx+xy2dx=xdy

⇒ xdy-ydxy2=xdx

⇒ -dxy=dx22

On integrating we get,

⇒-xy=x22+C

∵ It passes through (1,-1).

∴ 1=12+C ⇒  C=12

∴ x2+1+2xy=0  ⇒  y=-2xx2+1

∴ f-12=45

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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.