JEE Main 2024 Mathematics question
If the solution y(x) of the given differential equation (eʸ + 1)cos x dx + eʸ sin x dy = 0 passes through the point , then the value of is equal to .
Answer: 3
Solution
Separating, eʸ/(eʸ + 1) dy = −cos x/sin x dx gives (eʸ + 1) sin x = C. At (π/2, 0): C = 2. At x = π/6: (eʸ + 1)/2 = 2, so eʸ = 3.