JEE Main 2019MathematicsDifferential EquationsEasyMCQ

JEE Main 2019 — Differential Equations Question with Solution

JEE Main 2019 (12 Jan Shift 2)

Question

If a curve passes through the point 1, -2 and has slope of the tangent at any point x, y on it as x2-2yx, then the curve also passes through the point

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Show full solutionCorrect option: A
Correct answer
A3, 0

Step-by-step explanation

dydx=x2-2yx

⇒dydx+2xy=x.  It is in linear form.

I.F.=e∫2xdx=e2lnx=x2

∴y.x2=∫x.x2 dx=x44+c

∵At x=1, y=-2,

∴-2×12=144+c

⇒c=-2-14=-94

∴curve is y.x2=x44-94

∴It passes through 3, 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.