I9S DE CRITERIIS INTEGRABILIT. 



(p[(l - a + x'^y\{n+ 1 )^-(/// + i ) Y)) + (g) (Pj+^ -vV+O 



Kiinc \eio cuidens eft , huic aequationi l:\tisficri, 

 fi ftatuatur (p — .v^y , quo fecflo erit 

 (^):^H.v''-y et (J-|)rzX.x«j^-' 



hisquc valoribus introdudis et tota acquatlone per 

 x^^y^ diuifa , fiit 



(3 - a -i- ^'"fi (« + i) <J - (?;; -H I ) y) + X p - K flt 



+.vV(>vy-^y) = o. 



Hinc autem obtinemus 



l°p-anKa-X(3; IP f«+ i)J-(w+ i)y^hV-^^ 



cx priori fit(3(i-l-X) — a(i+H), ex pofte- 



riori \ero 



J(i-V-«-HX)— y(i-Hw + k-) , fiue 



?^( r + ;2 + X)=;a7/; + a( i +k) — a;;; + |3( i + X), 



crit igitur 



a{$fi-ym)-((iy-aSit + r„ vnde i+Xr?^^ 

 fimilique modo i -f- k := ^^JiLr-JL^-), 



Intcgralc autem aeqn;itionis propofitae nunc inuc- 

 nieiur 



Practerca autem crit 



+/Ayfa^;' + .v'"-'y((w+!)Y-^y>' + W(5'j')) 



AN^/jt- 



