VIFFERENTIAUBFS SECrNDl GKAD. i8i 

 Cum igitiir fit : 



crit nofler muitiplicator : 



—y tf\v ( (3 -h Y X) ~\-dy{a-^-2^ x H- y x x) 

 et integrale quaefituni habcbitur : 



-ydxdyip+yx^-^yy^a+i^x+yxxy^ji^^^-zpnx^^) 

 -^- '^y yy d X' zziQ d x^- 



At fi ponntur CmTr-l-C, erit hoc integrde : 



i YXKrt^jjT^-j^^.r/yd^ -f y X) -^\dyXa.-\-2^x-+yxx) 



' ayy dx-^ — ^/^1"^ 



— T" z[(z-i-2^.x-\-'y X X -\-c y y) v- M >A. . 



Qiiae forma conuenit cum ea . quam fupni exhibui. 



Theorema 2. 



24.. Ifta aequatio difF.remialis lecundi gradus pa- 

 fito dx conflante 



ddy H- ■ „ H^ = o 



integrabilis reddetur per trultiplicatorem : 



—ydxi^-^-yx^-^-dy^a-^^^x-i-yxx) 



et integrale erit : 



1 yyy dx^-y dxdy{^ -i-yx)-hl dy\a~\- 1 ^x-\-yxx) 



ay^^^^dx' 

 ^ ^^ — C dx\ 



{n 4- 2), ct -h 2 j3j: H- Y .r .v -+- ^/i'j ^ 



Coroll. I. 



2.^. Cafus problematis nafcitur ex Theoremate 

 hoc, {i ponatLU- «zno. Ceterum integi-ale in Theore- 



