JEE Main 2021MathematicsDifferential EquationsMediumMCQ

JEE Main 2021 — Differential Equations Question with Solution

JEE Main 2021 (27 Jul Shift 2)

Question

Let y=yx be the solution of the differential equation x-x3dy=y+yx2-3x4dx,x>2 If y3=3, then y4 is equal to:

Choose an option

Show full solutionCorrect option: B
Correct answer
B12

Step-by-step explanation

x-x3dy=y+yx2-3x4dx

⇒xdy-ydx=yx2-3x4dx+x3dy

⇒xdy-ydxx2=(ydx+xdy)-3x2dx

⇒dyx=dxy-dx3

Integrate

⇒yx=xy-x3+c

given f3=3

⇒33=3×3-33+c

⇒c=19

∴yx=xy-x3+19

at x=4,y4=4y-64+19

15y=4×45

⇒y=12

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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.