NTA Abhyas JEE Main2020MathematicsDifferential EquationsPractice
The solution of the differential equation 3 sin 2 ⁡ x cos ⁡ x y 2 d x + 2 y sin 3 ⁡ x d y = sin ⁡ x d x is (where, C is an arbitrary constant)
Options
- A2 y 2 sin x = cos x + C
- By 2 sin 3 x + cos x = C
- Cy 3 sin 2 x + sin x = C
- Dy sin x = cos 2 x + C
Correct answer
B. y 2 sin 3 x + cos x = C
Step-by-step solution
The given equation is d y 2 sin 3 ⁡ x = sin ⁡ x d x On integrating, we get, ∫ d y 2 sin 3 ⁡ x = ∫ sin ⁡ x d x ⇒ y 2 sin 3 ⁡ x = - cos ⁡ x + C or y 2 sin 3 ⁡ x + cos ⁡ x = C