DIFFERENTIALIBFS. J3 



_> H-/ dx- 80- -4- *&$&. 



//»_!- _^2 — ___L _l_ ______ 



quae omnes flint integrabiles. Quare haec aequatio dy-\~ 

 Ay 2 du~~\ B u u du -\- C du integrabilis exiftit , quando 

 - V £ fuerit numerus integer affirmatiuus impar , namque 4--f-_- 

 H- 1 omnes numeros impares complectitur in fe. 



§. ip. Ponamus in fuperiore aequatione tantum £;___: 



ffx 2 n d x 

 0; et prodibit ifta aequatio dy-\-xf dx~ ~T~~t 



_3* Ci C-c 1 1 * 



«^* . , ... • • ^ .-«-J-VCCp-f-i )«--«) 



quae lntegrabilis ent , quoties fuerit- 



numerus integer affirmatiuus , quifiti, erit ergo n (2/-J-1) 



— V((p-\-iY — a) atque a __=(/>-{- 1 )*—« 2 ( 2/-f- 1 )\ 



. ffx in -^~ 2 d x 

 Quamobrem haec aequatio^ ~{-x*y dxzzz -f. 



' -£-- femper mtegrabilis ent. Si fit 



p~o , erit ifta aequatio ,/j ~f-jV#____ 4 ^ a* 27l ~ 2 </;_-,- 

 <w * (at ^xx~' ? " pariter femper integrabilis. Hinc ponendo 

 4 -f a zzA, quia f et # funt quantitates arbitrariae , integra- 

 biles erunt fequentes aequationes 



i{i-+-i)dx 



dy -\-f dx—Ad x 



XX 



dy-\-fdx~-,kxdx-\- ( ^5 

 <T -h/ dx — kx 4 dx -4- ^^H? 

 atque huius generis innumerabiles aliae. 



G 3 §.20 



