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Which of the following represents the solution of the differential equation dy/dx + (y/x)\,log y = (y/x^2)\,(log y)^2 ?

1. y = log(x^2 + cx)
2. log y = x(cx^2 + 1/2)
3. x = log y(cx^2 + 1/2)
4. None of these

Correct answer: log y = x(cx^2 + 1/2)

Solution

The correct option represents the solution because it correctly rearranges the terms of the differential equation and integrates them, leading to a valid expression for y in terms of x, which satisfies the original equation.

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