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Given (2 + sin x) dy/dx + (y + 1) cos x = 0 with y(0) = 1, find the value of y(pi/2).
- 4/3
- 1/3
- -2/3
- -1/3
Correct answer: 1/3
Solution
Separating and integrating gives (y+1)(2 + sin x) = constant = 6 from the initial condition; at x = pi/2 this yields y = 1/3.
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