Verified Solution • 2025–26 Session moderate

QJEEM24Ma081e: JEE Main 2024 Mathematics - Class 12 JEEM24Ma081e Solution: Let y = y ( x ) be the solution of the differential equation…

Let y=y(x) be the solution of the differential equation sec⁡x dy+{2(1−x)tan⁡x+x(2−x)}dx=0 such that y(0)=2. Then y(2) is equal to:

Multiple Choice Options

  • A 2{sin⁡(2)+1}
  • B 2
  • C 1
  • D 2{1−sin⁡(2)}

Step-by-Step Verified Solution

dydx=2(x−1)sin⁡x+(x2−2x)cos⁡x

Now both side integrate

y(x)=∫2(x−1)sin⁡xdx+[(x2−2x)(sin⁡x)−∫(2x−2)sin⁡xdx]y(x)=(x2−2x)sin⁡x+λy(0)=0+λ⇒2=λy(x)=(x2−2x)sin⁡x+2y(2)=2

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