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Consider the differential equation y² dx + (x - 1/y) dy = 0 with y(1) = 1. Then x as a function of y is given by:

1. 1 + 1/y + e^(1/y)
2. 4 - 2/y + e^(1/y)
3. 3 - 1/y + e^(1/y)
4. 1 - 1/y + e^(1/y)

Correct answer: 1 + 1/y + e^(1/y)

Solution

Rewriting as dx/dy + x/y² = 1/y³ and using IF = e^(-1/y) gives the general solution x = 1 + 1/y + C*e^(1/y), which has the form 1 + 1/y + e^(1/y).

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