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A curve y = f(x) passes through (1, -1) and satisfies y(1 + x y) dx = x dy. Find f(-1/2).
- 4/5
- -2/5
- -4/5
- 2/5
Correct answer: 4/5
Solution
Solving the Bernoulli equation gives 1/y = -x/2 - 1/(2x); applying y(1) = -1 fixes the constant, and at x = -1/2 we get f(-1/2) = 4/5.
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