Definition :

An equation in differential form M ( x, y) dx + N (x, y) dy = 0 is said to be homogeneous, if when written in derivative form

there exists, a function g such that .

A homogeneous equation can be transformed into a separable equation by a change of variables.

The equation is homogeneous,

since

.

Take the transformation y = vx and

Then,

Separating variables,

Integrating,

Replacing v = y/x,

.