278 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 
rently without any sacrifice of generality, by the introduction of a relation be- 
tween A and B. The relation is, gee 
Hence the complete solution of the equation 
dt y 
ion 
ody 
ytaxnytbhea ee: 4+2ax qe = 
eiakes Pte) (at beled) Lhe 


= ly 
19. Ex. 3. Paton Tae 

=—3 
To (a4 bx) “Y 1954 356, 
dx- 
Multiply by «—%, and the result will be 
a? i ly —2 —3 
a2 y+anu-2 tears @ 234.6 2-2) @ Pate pt2be-% 549 
of which the symbolical form is 
—26 _,/—D-1 =) oe 
Vein Be waa SG CR" 4h) a ry 
1 /- 

which is equivalent to 


vs OF LP 1 ) -1 ( 1 2 
ee et GS neat (D+1 (D+2)) 7 +1) D+2- Ds) 1D Ws9) 9= 
24 Ale — 1 = 
or He EERO ya! Pay aan 
Hence, by multiplication, 
a iL 1 9 
-5(D+2) (D+3) e-* 4 y—| (D+2) (D+3) e-24 y=0 
1 
or —F (D+2)e~4 y— (D+2)e~* (D+.2)e~" y=0 by (B) 
which is of the form ( ty > 2 79”) ys 
which, being put under the form 
(l+a@) (1+@¢)y=0 gives 
y=A(l+ag)-!.0+B(14+6¢)-! 
Now (1+a¢)~'.0 is the solution of the equation 
aad 
y,+a(D+2)y,e- ’=0 ONT = 

= 
: Be ge 
of which the result is n=> e *, 
