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NTA Abhyas JEE Main2020MathematicsDifferential EquationsPractice

If the curve satisfies the differential equation x d y d x = x 2 + y - 2 and passes through 1 , 1 , then it also passes through the point

Options

  1. A4 , 4
  2. B3 , 3
  3. C2 , 2
  4. D0 , 0

Correct answer

C. 2 , 2

Step-by-step solution

The given equation is d y d x + y - 1 x = x - 2 x Integration factor = e ∫ - 1 x d x = 1 x ∴ the solution is y 1 x = ∫ 1 x x - 2 x d x ⇒ y x = x + 2 x + c As it passes through 1 , 1 c = - 2 ∴ y = x 2 + 2 - 2 x ∴ it passes through 2 , 2

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