The curve satisfying the differential equation sin ⁡ x 3 e y d y + 3 x 2 cos ⁡ x 3 e y d x = x sin ⁡ x 2 d x (where, C is the constant of integration) is λ sin ⁡ x 3 e y + cos ⁡ x 2 = C . Then, the value of λ is

Step-by-step solution

Given equation is d sin ⁡ x 3 e y = x sin ⁡ x 2 d x On integrating, we get, ∫ d sin ⁡ x 3 e y = ∫ x sin ⁡ x 2 d x ⇒ sin ⁡ x 3 e y = - 1 2 cos ⁡ x 2 + C or 2 sin ⁡ x 3 e y + cos ⁡ x 2 = C ∴ λ = 2