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NTA Abhyas JEE Main2020MathematicsDifferential EquationsPractice

The curve satisfying the differential equation x ln ⁡ x d y - y d x = x ln ⁡ x 2 d x is (where, C is an arbitrary constant)

Options

  1. Ay = ln ⁡ x 2 + C
  2. By = x 2 + C
  3. Cy = x ln ⁡ x + C
  4. Dy = ln ⁡ x x + C

Correct answer

D. y = ln ⁡ x x + C

Step-by-step solution

Given equation is ln x d y − y ⋅ 1 x ⋅ d x ln x 2 = d x or ∫ d y ln ⁡ x = ∫ d x ⇒ y ln ⁡ x = x + C ⇒ y = ln ⁡ x x + C

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