for Differential Equations of Mathematical Physics. 589- 



Hence 



£(r<*V)=0 (9.) 



dx l \ dec- I 



£&%)-»>■-> ^ 



From (9 ) it follows that 



A f« i'xdx pf* C*dx , n , n , 1m 



^ = Aj o ^J o -^+Bj o ^J o ^ + C. + I); . . (10) 



therefore 



Jo Jo -^Jo * 



= A dil -o 1 da? I da?/* J rf#l '-p- 

 Jo Jo K Jo ^o . o Jo **> 



f* i x dx ( x C x C x C x dx 

 Jo Jo -KJo Jo Jo Jo ■* 



r * r * dx c x c x r a r <r ^ r x 



4-Cl dtf) -n- I dx\ dXfJLX + D) dx\ r } \ fldx 



Jo o -^ Jo Jo o Jo ■" Jo 



etc (11) 



Inserting this expression for y y 1 ... in (8), y takes the 

 form 



y-=A J 5fx; + B/,(«5+(y,r*) + D/ l (*), . . (12) 



where 



Jo Jo K Jo Jo ttJo Jo Jo Jo tf 



( 7 * r« <^ r« Cx 

 d%\ "1 dtol //,a?da? + (15) 

 ^o *^o tv J Jq 



t 1 ® k® dr C x C x 

 dx\ * \ ^1 ^ + (16) 

 «/0 Jo tx Jo «■ 



The forms which these integrals adopt, although apparently 

 involved, are in reality very simple. It should be remarked 



