239 



inaj be written as: 



</> (*) = 'P, (^) + k' 'f, (*) + ^•" '/", (■^) + A" cp, {x) + 

 where 



X 



'Px («) 





{s)ds 



9 



r{x-sy 

 («) = — I ~§7~ '/' I (") * 



(x) — — i —^-j— 'In-l (») 



(is. 



This solution however can only graphically be used, if the 

 coefficients C' and D are known. Nevertheless this coeffioieiils depend 

 on the second and first integral of <f' {x) in a point which is different 

 from zero. Therefore we cannot find them a priori. 



4. To meet this difficulty, we introduce the function 

 X, (X) = g' + C,x+n,; 

 C, and Ü, being two constants, determinated by : 



I Xo (•^) d'" = 







J 



X. (•■«) -x dx = 0. 



By choosing C\ and D^ in this manner, we reach that 1°. Coand 

 D, can easily be graphically found, and 2°. that the function 



v>, (^) = — I ^-§7— X. («) t^» 



satisfies at the point x = I the conditions 



or the conditions 



I X. {x) d« = 0, j rf;i; 1 X. («) C^X =: 



