AEQVATK)WM BlWERENTIALlVAi. y* 



vnde integrale completum obtinetur : 



-i t i ""*. ""^* -i 



e^* Vstf-iS^+^tf^y-S+iS^ '-^occx '-\-15fx s ^, . 



J 7 ^T ^r: p_= Conft. 



($x~Yi5cx"-\-i5ccx* )y— 3-150: s -30«w s — 25/A: s 



Ac neglecto fa&ore exponentiali ^°«-« ^ produc*tum ex 

 numeratore et denominatore praebebit diuiforem , per 

 quem aequatio propofita diuifa euadit integrabilis. 



Problema 12. 



80. Denotante i numerum quemcunque inte. 

 grum , exhibere refolutionem buius aequationis : 



■ — ♦ ?' 

 dy -\-yydx—ccx* * •+• > dxzzzo. 



Solutio. 



Cum igitur fit nzzz 1 ^ , reperietur 

 E — LL±tl1L_ a 



/~> , (»-t- 2 ) (i,-4-i ) » '(»'_____ * 



* '+ 2 . 4 ( 2 Z-+-I )« c 2 A 



■r\ ( _f- 3 ) ( j -4- 2 ) (r-4- i )f C'i — 1 )( i - 2) \ 



**■—. 2. ... 6( 2 i-t- 1 )»c« A 



Tf . ( *-f-4 )(»-f- 3 )(*-+•? )(?-+- 1 )(:-■ )(*- 1 )( i°t ] » 



•^ — "T" ' 2.4. 6.a( 2Z-+-l)*C* A 



etc. 

 tum vero inregrale particulare crit : 



___ ~i~ l -i- t __-__ -'— +_ 



yzzcx 1 ^ 1 -\-~-^Ax**'- r J^Bx* i + , +^ 2 Xx*+'+-^Dx ti - + -'+ etc. 



^ ii+I _?l-4-l !_? Z-1 -? 2 1- +-1 



1 i—i i—2 i—z 



Ax^ 1 +Br IH -' +C.t J ^' -f-D^-i-' 4. etc , 



G 2 quod 



