Originally Posted by
Ackbeet You're welcome. Incidentally, there is a slight preference as to which substitution to use, merely as a practical matter. Let's say you write your homogeneous equation in the form
M(x,y) dx + N(x,y) dy = 0;
furthermore, let's say M is simpler than N. Then the substitution x = vy will often work slightly better than the other, although you will get a separable equation either way. If N is simple than M, then the substitution y = ux will often work slightly better. See Zill's A First Course in Differential Equations, 6th Ed., p. 55.