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MHT CET2018MathematicsDifferential Equations

The general solution of differential equation d y d x = cos ( x + y ) is

Options

  1. Atan ⁡ x + y 2 = y + c
  2. Btan ⁡ x + y 2 = x + c
  3. Ccot ⁡ x + y 2 = y + c
  4. Dcot ⁡ x + y 2 = x + c

Correct answer

B. tan ⁡ x + y 2 = x + c

Step-by-step solution

Let x + y = v 1 + d y d x = d v d x d y d x = d v d x − 1 ∴ d v d x − 1 = cos v ⇒ d v d x = 1 + cos v ⇒ d v d x = 2 cos 2 v 2 ⇒ ∫ d v cos 2 v 2 = 2 ∫ d x ⇒ ∫ sec 2 ( v 2 ) d v = 2 x + c ⇒ 2 tan ( v 2 ) = 2 x + c ⇒ 2 tan ( x + y 2 ) = 2 x + c ⇒ tan ( x + y 2 ) = x + c 2 ⇒ tan ( x + y 2 ) = x + c

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