the calculus of functions. 415 
an equation of the first order from which y may be found or 
thus assume 
$ y=x {y>f'y} 
and make/^y =y, 
this method is much more extensive in its application than any 
of those before it. 
Problem XVI. 
Required the solution of 
x — x 
the same method applies equally in this case, 
Assume -Ajx — pfpx 
then §' f n <px = x 
for x put <p x it becomes 
<P f n x = (p 1 X. 
Take (p 1 an arbitrary symmetrical function of 
oc,f n x 9 f* n x , and f kn x, 
then (p x=X | oc,f n oc,f°' n x, . . f kn oc | 
and determine f such that 
f{ k +') n x = x 
a particular solution is sufficient, and it is evident, this value 
of (p 1 will satisfy the equation. 
Problem XVII. 
Given the equation 
( y , vl jy) =y 
required the form of y. 
Assume ^ y == dp 1 f$y, then it becomes 
$ f<px(y, $ f(py) =y, 
