IN THE DIFFERENTIAL CALCULUS. 47 
By the usual process, this equation becomes 
D (D1) u—g 2c?’ w—i (¢+1)u=0 
(D+2) (D—i-] u—¢? ce?’ u=0. 
=e—tl ef (- >) ev, then 
(D+) (Dé 1) ef (— FZ) v—gre"4s(— 
or | D(D-2:-1)f (-Z)e- gf Dine» “ 
an equation which, by omitting the function of 0, is reduced to 
D (D-1) vq? e?4v=0 (1,) 
or 
Let 
P+ ee= 0 
by the condition 
per 
c-Fes (-F) 



/ ee 
wile 2 
and oe 


nS -i i41 (1 d\iv 
But the solution of Equation (1.) is 
v=A el*+Be-2": 
Hence the complete solution of the given equation is 
u=(—2)~* ait? (= iz) ; *(Ae*4B eat) 
This solution is susceptible of another form by Art. 11 ; for by that Article 
1 d\tv _,_4yi -@i+2)(.5d\* vw 
age ee) 
gri-l 

apt l_(,sd\i Adtt+ Bent 
Sel = erat ae 
VOL. XX. PART I. 
