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NTA Abhyas JEE Main2020MathematicsDifferential EquationsPractice

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

Options

  1. Ay + tan ⁡ x + y – sec ⁡ ( x + y ) = c
  2. By – tan ⁡ x + y – sec ⁡ x + y = c
  3. Cy + tan ⁡ x + y + sec ⁡ x + y = c
  4. Dy – tan ⁡ x + y + sec ⁡ x + y = c

Correct answer

D. y – tan ⁡ x + y + sec ⁡ x + y = c

Step-by-step solution

Let x + y = v d v d x - 1 = 1 s i n v d x = 1 - 1 1 + s i n v d v ⇒ x = v - ∫ ( s e c 2 v - t a n v ⋅ s e c v ) d v ⇒ x = v - tan ⁡ v + sec ⁡ v + c ⇒ x = x + y - tan ⁡ x + y + sec ⁡ x + y + c

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