VIFFERENTULIBFS SECFNDI GRAD. 199 



,d^X . 



Cui aequationi \t fatisiiaty ponatur Bzro; et (^— jjzio 

 feii 



X~a-\-zpx-i-yxXy, fiatque ^_n^,^{n+z) -^ (^iio-* — o 

 fiue nzi:~§. 



\nde erit r. 



P— 36 Aj^f p -+■ Y ^)- Qiiare haec aequatio difFerentio* 

 diffeientialis ; 



— i ■ 



ddj ~\-y ^dx-{a -\~2 g>x-\-y xx)zzo 



fit integrabilis y fi multiplicetur per 



3 6jP{g,-{-yx)dx''-i 2y '[^a-\-2§x-\-YXx]dx^dy+^df 

 et integrale erit 



3 ^/( p+ yx)dx'dy- 6y %-Jt- 2 pA,'+7A''^y^A,'^^*"4-^J'^' 



— * t 



-I- 9 y '(a+ 2 (3 .r-i yxx) Vjc*- 2 -jyy'dx'zz.Qdx'' 



atque in hac lolutione continetjir exemplum quartum 



CorolL r. 



38. Qiiartum ergo exemplum fupra- allatuni' 

 aequationem difFerentiakm maxime memorabilem con- 

 tinet » propterea quod ea nonnifi per fadorem tertii 

 orainis ad integiabilitatem perduci poteft , \nde eius.^ 

 integratio multo minus ab aliis meihodis expedari 

 potcll. 



Coroll. 



