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For the differential equation dy/dx = [y f'(x) − y²]/f(x), where f(x) is a specified function, the solution is

1. f(x) = y(x + c)
2. f(x) = cxy
3. f(x) = c(x + y)
4. y f'(x) = cx

Correct answer: f(x) = y(x + c)

Solution

The correct option represents a relationship where the function f(x) is expressed in terms of y and a constant, which aligns with the structure of the given differential equation, allowing for separation of variables and integration to find a solution.

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