JEE Main 2021MathematicsDifferential EquationsMediumMCQ

JEE Main 2021 — Differential Equations Question with Solution

JEE Main 2021 (26 Feb Shift 2)

Question

Let slope of the tangent line to a curve at any point Px,y be given by xy2+yx. If the curve intersects the line x+2y=4 at x=-2, then the value of y, for which the point 3,y lies on the curve, is :

Choose an option

Show full solutionCorrect option: C
Correct answer
C-1819

Step-by-step explanation

Given dydx=xy2+yx

xdy-ydxy2=xdx

-dxy=xdx

-xy=x22+c

∵ Curve intersects the line x+2y=4 at x=-2⇒ point of intersection is -2,3. 

∴ Curve passes through -2,3. 

⇒23=2+c⇒c=-43

⇒-xy=x22-43

Now put 3,y we get, 

⇒-3y=196

⇒y=-1819

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About this question

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.