Theorema II. 



§. 49. Si haec aeqnatio difTcientialis : 



d X i_ dy 



H- .-7-r^^-:;— = O 



ita integretur, vt pofito j — o fiat xzzky integrale fupra 

 triplici modo eft inuentum ; erit enim : 



T &-f- c (^ -f- j') b 4- c fe . •. 



c jcj> — u a • ' 



11 g (j: -^- - v) -H & j,- y — r 



c X y — a 



TTT fc-Hc ( .. +y) b -hck 



a^x+yy-h b xy ak 



Theorema III. 



§. 50. Si haec aequatio difFerentiahs : 



^_^ d^y — -o 



V (A-(- B jc-i- Cx x) ■[/ {.\ + Ky-t i-'yy) ~ 



ita integretm-, Vt pofito j — o fiat x — k, integrale erit 



— B {x 4- j) - 2 C .vj + a V (A + B .V + C .v .v) 



y {A^By-hCjj)- 

 -Bk + 2y A {A.-\-Bk-\-Ckk)y fiuc 



B{k-x -j) - 2 C A-j - 2,y A (A -I- B k-^CMl 

 — ^y (A -f B X + C x-x). (A + B j' 4-' C jj) [ 



Corollarium. 



§. 51. Hinc ergo patet, fi aequatio differentialis 

 propofita, fucrit ifta:' 



^=Li , - <^y ■ - o 



V (A -(- B x-f C * xJ ~ y (A -HB3-+-Cj)'3') "^ ' 



eaque integretur ita, vt pofito j/ z: o fiat x~k, integrale 

 fare 



B {k — X —j) — 2 C .V y 3 2 y (A + B -v + C X x) 

 y (A + B j + Cjjj -z-V A{A-{-Bk^\-Ck k). 



'1 ' ' Theo- 



