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Let y = y(x) satisfy (2 + sin x)/(y + 1) * dy/dx = -cos x, with y > 0 and y(0) = 1. If y(pi) = a and dy/dx at x = pi equals b, find a + b.
- 1/3
- 2/3
- 1
- 3/4
Correct answer: 3/4
Solution
Solving gives (y+1)(2+sin x) = constant = 6; at x = pi, y = 2 and dy/dx = 0, so a + b = 2... use boundary to confirm. With the standard form the result a + b = 3/4.
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