I 
the calculus of functions. 
23 1 
Jl 
Ex. 2. Given the equation x n fyx — afy — = 
here = — and a 2 x=zx, and we have 
tftcV 
bxf — #%]/• 
AT 
X 1 
and putting ~ for x it becomes 
44 = 
bx p —a 
x 
Substituting this in the former equation we find for the value 
of t[/X 
4 ' x ™ TZx { x ^~~ n + ax ~~ p } 
Ex. 3. Given the equation x n 4/ x~x m xj/ f 2—Z) s= j# 
by employing the same method its solution will be 
(#) 
ln£. I/ 
I-r-CX 
+ 
\ i—cxj 
x 
a — x \n 
I —cx 
a.’—x \ ’ 
x — — - 
l*—cxj 
Problem XXXII. 
Given the equation 
F | x, \|/ x } x\j u x, . . i[/ u n x | = 0 
and also «*+« = x 
putting successively x , c&x, <x,*x,8cc. a. n x for x, we have the 
following equations : 
F -tyx, ip a X, . . \p c& n X l = 0 ^ 1 ) 
F | a X } 4/ a, X, fyo? X 3 . . x|/ cc n X, tyx J = 0 ( 2 ) 
&c. Sec. 
F jVx, $* n x 9 $x t $ux, =30 (ft+l) 
