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MHT CET2017MathematicsDifferential Equations

The particular solution of the differential equation x d y + 2 y d x = 0 , when x = 2 , y = 1 is

Options

  1. Ax y = 4
  2. Bx 2 y = 4
  3. Cx y 2 = 4
  4. Dx 2 y 2 = 4

Correct answer

B. x 2 y = 4

Step-by-step solution

x d y + 2 y d x = 0 ⇒ d y y + 2 d x x = 0 On integrating ∫ d y y + 2 ∫ d x x = C 1 log ⁡ y + 2 log ⁡ x = log ⁡ C ∴ x 2 y = C When x = 2 , y = 1 , C = 4 ∴ Particular solution is x 2 y = 4

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