fji Opuscula. 
Subftitutlones alix x = /"'^^ = e^"'^^ fimiliter in- 
fervire polfunt refolvendx aequationi x d^ x — {a -\- i) d x^ 
-\-bdxdz> — cdz^zmo. Radicatus Comes clariiruTius , quo- 
cum Lexellii problema per litteras communicaveram , no- 
vam , atque ingeniofam methodum aliam excogitavit , qua 
triuni conftantium additione propofita xquatio , & tribus 
integrationibus ad finitam formam reducitur . Qux metho- 
dus cum generalis fit , & varios cafus comple6i:atur pro va- 
rietate coefficientium xquationis , fingillatim in hoc fpeci- 
mine exponi debet . 
Cafus prior y 
in quo tO. a =. — 2 , 
Proponatur xquatio dyd^ y — 2 d^ yd^ y-\-hdy^ d^y-{-cdy^=Oy 
caque multiplicetur per e dy ~^ ^ & fit e iile numerus , 
cujus logarithmus elt unitas . Prodibit acquatio alia 
{dy ~^d^ y — 2 d y~^ d^ y d "^y -\- b d y~~ ^ y-^-c dy)~Oy 
& pofita M conftanti quantitate , integrando habebitur 
idy-"- d''y-\--^)z:zM, 
Multiplicetur rurfus aequatio per e^^^^ dy^ & fit 
p. 4. 'JJ ^ Me-hdy. 
Pofita dx conftante , & N. accepta pro conftanti alia quan- 
titate, fecunda integratione orietur 
atque a logarithmis ad numeros tranfeundo erit 
f Me -|_ cy-\-K\ 
^^T=fe dy, 
Cafns alter ^ 
in quo a z=z — 2,&^=o. 
Si fit =r — 2 , &c b = o , erit propofita aequatio 
dy d^y — 2 d^y d^-y -\- c d y'^ — o , 
eaque 
