AEQVATIONVM DIFFERENTIALIVM. 3? 



ficque integrale completum noftra<e aequationis efiV 



— e~ x - x dx „ n 



TTZ -, -+-/* ~ = Conff. 



Exemplum 2. 



67, Inuenire multiplicatores idoneos , qui red- 

 dant hanc aequationem integrabilem i 



Cafus fmgularis huic aequationi fatisfaciens efli 



v — ■ »-*-!«: ~ 



J — a. -f- (3 x -+-y x x. w 



exiftente k =z 1 (3 + V ( \ (3 (3 - a y -f- <7)\. 

 Cum nunc fit P~ o, et Q_— 1, erit. 



A y x + 2 *y x d x 

 S~ f ^a + px + Vti 



vef pofito breuitatis gratia __hV(l^^—ay^a)z=:lm 

 eiit 



f___n£x_ 



S r i ^ -'aHr-P^-+-7*».' 

 — a-+(3x-+-'y •«* 



/- na x 



Mulriplicator ergo primum inuentus eft 



r nd x 

 Jan 



J&.-+-P*-i-yx x. &-+ -&x- j-yxx 



( (a+- $x-t-yxx) y—. k — yx) 2 



qui porr® duci potelb in functianem quamcunque huius 

 quantitatis, 



J~~«'a-+-|3-c -i-yxx f i i Y 



\(<x.-t-Px-i-yxx)y — fc, — y x. l n 1" 



Ducatnr ergo in 



y nd x 

 , a -+-£*-+■"> xx' ( g + ga-H-i/ xx)y — k — yx 

 {<x-i-$x-i-yxx)y~i-n — k—yx. 



ac 



