(Homogeneous equation) The equationis said to be homogeneous because f (y/x) is homogeneou...

(Homogeneous equation) The equation

is said to be homogeneous because f (y/x) is homogeneous (of degree zero); see the preceding exercise. CAUTION: The term homogeneous is also used to describe a linear differential equation that has zero as its “forcing function” on the right-hand side, as defined in Section 1.2. Thus, one needs to use the context to determine which meaning is intended.

Show, by examples, that may, but need not, be separable.