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NTA Abhyas JEE Main2020MathematicsDifferential EquationsPractice

The solution of the differential equation sin ⁡ y e x d x - e x cos ⁡ y d y = s i n 2 y d x is (where, c is an arbitrary constant)

Options

  1. Ae x s i n y = x + c
  2. Be x = x + c sin ⁡ y
  3. Ce x ⋅ x = sin ⁡ y + c
  4. De x ⋅ sin ⁡ y = x 2 + c

Correct answer

B. e x = x + c sin ⁡ y

Step-by-step solution

Given equation is sin ⁡ y · e x d x - e x cos ⁡ y d y s i n 2 y = d x ⇒ d e x sin ⁡ y = d x On integrating, we get e x s i n y = x + c or e x = x + c sin ⁡ y

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