NTA Abhyas JEE Main2020MathematicsDifferential EquationsPractice
The solution of the differential equation 2 x e x d y + e x y d x = x sin x d x is (where, c is an arbitrary constant)
Options
- A2 y e x + sin x = c
- By sin x = e x + c
- Cy e x + sin x = c
- D2 y e x + cos x = c
Correct answer
D. 2 y e x + cos x = c
Step-by-step solution
The given equation is e x ⋅ d y + e x 2 x d x ⋅ y = sin x 2 d x or d e x y = 1 2 sin ⁡ x d x On integrating, we get, e x ⋅ y = − cos x 2 + c ' i.e. 2 y e x + cos ⁡ x = c