NTA Abhyas JEE Main2020MathematicsDifferential EquationsPractice
The solution of the differential equation y sin 2 x d y + sin ⁡ x cos ⁡ x y 2 d x = x d x is (where C is the constant of integration)
Options
- As i n 2 x ⋅ y = x 2 + C
- Bs i n 2 x ⋅ y 2 = x 2 + C
- Cs i n x ⋅ y 2 = x 2 + C
- Ds i n 2 x ⋅ y 2 = x + C
Correct answer
B. s i n 2 x ⋅ y 2 = x 2 + C
Step-by-step solution
The given equation is s i n 2 x 2 y d y + 2 sin x cos x d x y 2 = 2 x d x or d s i n 2 x ⋅ y 2 = 2 x d x On integrating, we get s i n 2 x ⋅ y 2 = x 2 + C