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The solution of the equation x dy/dx + y = 0 passing through the point (1,1) is

1. x
2. x²
3. x⁻¹
4. x⁻²

Correct answer: x⁻¹

Solution

The equation is a separable differential equation that can be rearranged and integrated to yield the solution y = C/x. Given the point (1,1), we find that C = 1, leading to the solution y = 1/x, which is equivalent to x⁻¹.

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