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If (2 + sin x) dy/dx + (y + 1) cos x = 0 and y(0) = 1, then y(π/2) is equal to:
- 4/3
- 1/3
- 2/3
- 1/3
Correct answer: 1/3
Solution
The differential equation can be solved using an integrating factor or separation of variables, leading to a solution that satisfies the initial condition y(0) = 1. Evaluating this solution at x = π/2 yields y(π/2) = 1/3.
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