HOMOGENEOUS EQUATIONS, 
whence, making 
which resolves itself into the two equations, 
The former gives on integration 
whence 
and now re - 
we have on reduction, 
A + Bx K h 
A and B "being arbitrary constants. This is the complete 
primitive. 
The remaining equation u = 0, or ^ = 0, gives z = c, or 
y — cx, and this is the singular solution. 
The equation (a) might have been directly deduced from 
the given equation by the general theorem (19), which indi 
cates that for such deduction it is only necessary to change 
x to 1, y to 2, ~ io u+ z, and to u~ + u. 
Class II. Equations which on regarding x as of the first 
el'll d 2 v 
degree, y as of the n th degree, ^ of the n — 1 th degree, ~ of 
the n — 2 th degree, &c., are homogeneous.