JEQVATIONFM DIFFERENTIAUVM. 45 



quo debite fubftituto obtinebimus : 

 orz w(«— i)Aa?"" I -i-(3»-i)(3«-a)Bji: 37l " s -+(5«-2X5»— 3)C* sn "*-T-etC 

 -±2ncPLxr n - 1 +z(zn-i)c 1 &-\- z($n — *)cQ -4- 2(7«- 3, (cD 

 -~2nc\—zncB — 2bc C — 2/nD 



vnde coefficientes ficti ita determinantur : 



ft ( 2 »-x>B-t-»(*-i}A=o ; Bzz^fe^ 

 2( 4 «-2XC-f(3«-i)(3«-2)B-o; C=^^5=^ 

 2(6w- 3 >D-4-(5«-2)(5«-3)C-o^ D=~-^^f C 



Statim igitur atque vnus coefficiens euanefcit , fequentes 

 fimnl omnes euanefcunt , id quod euenit his cafibuar 



»—0; n — \; « = f; nzz%; etc. 

 '£2 « = x; «=f; « = f; nzz±-, etc. 

 Denotante igitur i numerum integrum quemcunque ,, 

 quoties fuerit nzzL ——z , - , toties refolutio aequationis 

 exhiberi poteft. Erit enim yzzcx~~* n + ^T^» exiftente 

 5f=A^ H -+-B^ lB - f H-C^ s *-" 2 -4-D*' B -- , --HEa: 9B ""*-Hetc. 

 Proueniet ergo hic valor particularis ipfius j : 



«Aj n -H-(3K-*)B* 3n - 2 -f(5K-2)Cr 5rt -' 

 j—cx "*+ Ai ; -^, b* jH -'-*-C* sH - 2 +ctC ' 



Coroll. 1. 



71. Quodfi ergo ifte valor particularis ipflus j» 

 vocetur zi;, efit aequationis propofitae multiplicator 

 idoneus --,-»/<>**. _J__, Ac fi ponatur/*-*/^*^ 



F 3 =V, 



