PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. O78 


n— D+ 
which is equivalent to y yet Oe aero 26 /— 


=== 0 
a 
4 26 rdiay 1 _ 
or Oe Cee =0, or, if v=zy, 
2b ,@ »v Pee : , ; 
v + =— x” — =0, which is the form integrated in Class 1 
3a dau? 
b= ee 5 =n, equation (2) becomes 
Dh din ep {/=D+n (n—4)6 
Zo) Gig BA Set —0 
which is equivalent to y + —_,—— a alle ere ea z y=0 
= 
: 2b ,dby 
which is of the same form as in the last case. 
B. If ¢ is not equal to z, we have from equation (1) by (D.) 
CMOS re ca ee DE D+n (1+e D—en) 




_ o(— 48 0 
/—D+n—-4 ; aes 
—-l+eD-—cn /—Din i 
6b — = (m-3)b yy — 
yro¥—l ey a0). =) caer ie 
3. If re =a this gives 
—Een 
yt+b/—1 (1l-en) ——— .y=9 
db y 
or yt+b(l—cn) a” —— Jab = the same form as before. 
16. It would be improper to dismiss this equation without remarking the 
fact that it would appear to have been solved by M. BesGE in LiovuvILue’s Jowr- 
nal 1844, ix., 294. The solution is, however, given without any demonstration, 
and is, if I mistake not, rather a differential equation jormed than a differential 
equation solved. The whole which appears is as follows : 
66 1 6) diy dy d? Y 
Let m, n, p, q be functions of w, and 7 t™ ne ca te ae the 
proposed equation. 


“If we have a +mn—p=0, the given equation can be reduced to the follow- 
5 bs : . : d ” 
ing, ot +my=z, where z is obtained from the equation at nm 2=9- 
a 
aa 
VOL. XVI. PART III. BoZ, 

