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MHT CET2017MathematicsDifferential Equations

The solution of the differential equation d y d x = tan ⁡ y x + y x is

Options

  1. Acos ⁡ y x = c x
  2. Bsin ⁡ y x = c x
  3. Ccos ⁡ y x = c y
  4. Dsin ⁡ y x = c y

Correct answer

B. sin ⁡ y x = c x

Step-by-step solution

d y d x = tan ⁡ y x + y x y x = v y = v x d y d x = v + x d v d x ∴ the given equation becomes v + x d v d x = tan ⁡ v + v 1 tan ⁡ v d v = 1 x d x ∫ cot ⁡ v d v = ∫ 1 x d x log ⁡ sin ⁡ v = log ⁡ x + log ⁡ c = log ⁡ x c sin ⁡ v = x c sin ⁡ y x = x c

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