
PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 
The equation in 0 is 
which may be written /(—D)y=X; 
and y={f(—D)}-! . 0+ff(—D)}-! . X 
eS 6b, 27 
Tie se 
the values of n being determined by the aia f (n)= 
d™y “By 
Ex. 6. (aarp * +a(axv+)” —_7 + &e. 2) 
d a” 
Let 2 =a2+, then “2% =a" "4% (Part 1, Art. 27.) 
Oa Ol 
&. = ae. 
1 — ieee ie hy 
ae 7 + &e. oe 

Py 
Ex. 7. i ie 
By multiplying by 2 and reducing to differentials in 6, we get 

eu —— taVx(— pi /=D+s Set y+) Ly=0 
[- D 
= D+1 +5)y ge a pedi, Fy 30 









/-—D /-D+4 
—D+1 4 
or —D+4 ; _p! 2 y= 
(“Day ta(—1 aoe 
eS So 
or y+a(—l) Dri y= 
Fae 
or yta(—l1)’ e aah 0 
or ielbu ogy ies aaeetlas) 2 
x =D * 
ew 
or Jig. 4 *#=0, 
© du-* 
VOL. XVI. PART III. 
69 
