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If k is a constant, the general solution of dy/dx - y/x = 1 will be in the form of

1. y = kx
2. y = kx + x ln x
3. y = kx + 1
4. y = kx + x

Correct answer: y = kx + x ln x

Solution

The correct option is derived from solving the first-order linear differential equation using an integrating factor, which leads to a solution that includes a term involving the natural logarithm of x, specifically x ln x, in addition to the homogeneous solution.

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