74 0. J. MALMSTEN, 



Satt for korthetens skull 



ny 



............................................................. (183) 



hvadan 



du (m + l)y' 8 + [(1 - r) ay' - mry] y" 





dv (n + l)y' 8 + [(1 - s)xy - nsy] y" 



~ ~~ 



afvensom 



Dw (1 r) xy' mry DM m 



= - 



to_ (1 - s)xy' - nsy 



' 



rfy " (y' 



Eqvationen (180) eller, hvilket ar detsamma, 



<p =f( v )-u = o ........................................................ (188) 



gifver differentierad 



Ora vi nu enligt theoreraet IX vilja finna integrations-faktorn , erhalles af (188) med till- 

 hjelp af (189) 



Dy du 3u DM 

 dy c/y rfy dy 



i>(f du Du DM 

 rfy' cZu c(y' eZy' 



d. v. s., om man far korthetens skull satter 



p = (l- s)(m + !)-(!- r)( + 1), ....................................... (190) 



q = ns(m + 1) mr(n + 1), ...................................................... (191) 



med tiUhjelp af (186) och (187) 



D^ 1 (n - m)y* + [(r - s - p) xy' - (ns - mr - q)y] y" 

 dy (y') r (n + l)y' 2 + [(1 - s) xy - nsy] y" 



' - qy _ 



dy " (yj~ l (n + l)y" + [(1 - a) ay' - nsy] y" 

 Haraf erhdlles 



