Show that the differential equation dy/dx = y^2/(xy - x^2) is homogeneous and also solve it.

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Show that the differential equation dy/dx = y2/(xy - x2) is homogeneous and also solve it.

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Given differential equation is

Thus, the given differential equation is a homogeneous differential equation.

Now, to solve it, put y = vx

On integrating both sides, we get

which is the required solution.