270 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 
iLie 2 =0; this gives 
-— d-ty 
dxz-t 
whence pa eee 
and y=va=Are”®. 
This equation may be integrated in the following manner. The equation 
D+1 3 Ls 
IDEN oy oy 
may be made to depend on the equation 


yal ee 
6 
e? v=0 

OB 
aA lire res? 
: D+1 /—D+4 
by the relation y=P, ae 2 5 v, Where 

P, f(D)=s (D) f D-4) f D-1) &e. ....... 
y=? 4 ” 
DO) =a. 
== ov - 
=F, ()= te 
= Dv 

ao e? v=0 is equivalent, by (D), to 
|= 
Now v+avVv—1 a yee Tea 
‘0-4 
we ON ROL ex fe v=0 

d-* 
or ae ae 
whence p= Ane 
y= Axe“* the same result as before. 
This process, which is due to Mr Bootg, is of great importance in the solu- 
tion of certain classes of ordinary linear equations, but I have not, as yet, found 
it very extensively applicable to equations with fractional indices. 
Ex. 8. More generally, to investigate the conditions of integrability of the equation 
dy ak OO 
Det aie ere 

