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If a curve y = f(x) passes through the point (1, −1) and satisfies the differential equation, y(1 + xy)dx = x dy, then f(−1/2) is equal to -
- 2/5
- 4/5
- 2/5
- 4/5
Correct answer: 4/5
Solution
The differential equation can be rearranged and solved using separation of variables, leading to a solution that incorporates the initial condition given by the point (1, -1). Solving this yields the specific function f(x), and evaluating it at x = -1/2 gives the correct value of 4/5.
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