The equation (αxy³ + y cos x) dx + (x²y² + β sin x) dy = 0समीकरण
The equation
(αxy³ + y cos x) dx + (x²y² + β sin x) dy = 0
is exact for
समीकरण
(αxy³ + y cos x) dx + (x²y² + β sin x) dy = 0
बिल्कुल सही (exact) है
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Correct answer: (A) α = 2/3, β = 1α = 2/3, β = 1 के लिए
Explanation
Exactness needs ∂M/∂y = ∂N/∂x: 3αxy² + cos x = 2xy² + β cos x. Hence 3α = 2 and β = 1, i.e. α = 2/3, β = 1.यथातथ होने के लिए ∂M/∂y = ∂N/∂x चाहिए: 3αxy² + cos x = 2xy² + β cos x। अतः 3α = 2 और β = 1, यानी α = 2/3, β = 1।