the calculus of functions. 215 
Ex. 2. Lett]; 3 ’ z (x,y) ~ y 
put a {x,y) = ^ and &(x,y) =y 
then the equation to be solved is q > 3 v = v a particular solution 
of which is <pv = putting for v its value and using the 
the general solution we have 
^{x,y) = (p< 
f-T 1 ! 
1 x 1 
1 — 3 <P — I 
L * j 
> 
as a particular case, take 
. , x f V* + x n 7 n 
^ y ) *“ 1 -3 **» } 
which will be found on trial to satisfy the condition.. 
Problem XIX. 
Given the equation 
f {7 (£,2), t!' • • ¥ ,p {x>y) ) = <> 
This equation is evidently capable of solution by the same 
means as the last ; putting 
,, x J 0(1, 1) («^lX 
n — m 
K — -±'m 
we have as before 
1 
— m 
« O y) 
and assuming a, and /3 such that t- = y (x, y) = v 
p ■ ’2Jm 
and 
