= Solution
The equation is \b[not separable], because $x^2-xy=x(x-y)$ cannot be written as a product of a function of $x$ and a function of $y$ on an open region. For example, the ratio $(x^2-xy_1)/(x^2-xy_2)=(x-y_1)/(x-y_2)$ depends on $x$ for distinct fixed $y_1,y_2$, whereas a separated product would give a constant ratio.
It is \b[not homogeneous] in the sense of a <homogeneous first-order differential equation>: the right-hand side is not a function of $y/x$ alone. It is also not a <homogeneous linear differential equation>, since moving the $xy$ term to the left leaves a nonzero forcing.
It is \b[linear], since it has the standard <linear ordinary differential equation> form
$$
y'+xy=x^2.
$$
Thus the classifications are \b[(a) no, (b) no, (c) yes].
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