PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 251 
Suppose y=34,,e""; then by (A) 
36, (m —a*) e”*=0; which can only be satisfied when =a. 
y=Ae’” is the solution of the equation. 
We might have proceeded in a somewhat different manner, as follows: 
Put 0¢”” for 0, then 
MX 


Dae: aay. : i : by (A). 
m —a 
But a a is finite only when m=a; and then it is constant; .. y=Ac*”, 
as before. 
Ex. 2. — y=X,; X being any function of z. 
We have y=(d!—a!)"!. X+(a*—-a})"* . 0. 
if X=%b,e" 

b “#5 
gee > 2 e* (Ex. 1.) 

r rv . . . . 
Cor. 1. Ify =a, ~—je becomes infinite. In this case put «+a in place of r: 
r —a 
atltaxe+a&c. 
a 
2 at + &e. 

b : 
then. = 2 =Ge becomes 4, ¢ 
r—a 
2 x 
ea on 42 a awe , when a=0; 
a 
aX 
of which the first term may be incorporated with A e 
tion is 
; and the complete solu- 
b est 
s 
ae 
y= Ae "+2 b, a? re eS 

Cor. 2. If X= x2”, we have, by the well-known formula 
a0 
ay eee a”™-1 da, 
fue |n 7) 
PE ON hewialige 7° Sagi eae 
(d*—a*) ae aera by (A.) 
b 2 
---f{* ee + ie.) “a da 
|n SJ o a a” 
a 
