AEQKfflONm DIFFERENTIALIVM. 3* 



Inuento autem vno diuitlore, (eu multiplicatore , ex eo 

 leperientur facile omnes poffibiles. 



Coroll. r. 



£3. Forma ergo diuiforis, per quem aequatfo 

 dirTerentialis 



( a+- p x +- y y ) dx +- ( $ +- e# +- %y ) ^ = © 

 redditur integrabilis , eft 



pjt Jir-4- (y +- e )>.* +- %yy-\- A #-1- B^-f-C 

 ^bi eonftantes A, B , C fupra funt deflnitae 



Coroll. 2. 



54. Cum diuifor inuentus etiarn fatisfaciaf , & 

 per ye—fiZ multiplicetur r patet, cafu, quo {3£— ye, 

 diuiforem fore 



(aee-(3£e+-(Ty 'f— a{3£)*+-(y y #' — « y£ 



+ ae£-££'£)^+ay £-««£ + «$€-£££• 



<gui pofito ^—mf\y=znJ\t—mg\Xzzzng 9 abit in 



MX*&-?f,)(mg-i:f)x + n{ag-$f)(mg-nf)y 



-+ ('«£.— $f) (tm — *n) 



CorolX 3, 



^5. Quare fi aequatio propofita fiierit huiusmodi : 

 (ct+f(mx + »j* )) </x+ ( £ 4-£ ( 7» x+ »j^ )) </y.~ o 

 «a reddetur integrabilis , fi diuidatur per 

 (.«£—»/ )(«*+- »7 )+-&«-«*».• 

 fiue per wx+ »j^*+-l|Efi§i At fi fuerit mg*-nf=o r 

 aequatio jpropofita iam ipfa eft intxgyabilis,. 



Erob* 



