NTA Abhyas JEE Main2020MathematicsDifferential EquationsPractice
The solution of the differential equation y cos ⁡ x . d x = sin ⁡ x . d y + x y 2 d x is (where, c is an arbitrary constant)
Options
- Asin x = x y 2 + c
- B2 sin x = x 2 y + c y
- C2 sin x = x y 2 + c
- Dsin x = x 2 y + c y
Correct answer
B. 2 sin x = x 2 y + c y
Step-by-step solution
Given equation is ycos ⁡ x d x - sin ⁡ x d y y 2 = xd x or d sin ⁡ x y = xd x ⇒ ∫ d sin ⁡ x y = ∫ xd x ⇒ sin ⁡ x y = x 2 2 + c ' o r  2  sin ⁡ x = x 2 y + c y