Al-101 ^t-7 



Particular solutions of (35), (36) are 

 1/3 ^ 1/3 



^ 3 ^3/3 



The homogeneous solutions may be derived by letting 



V° = Ae^^, V° = Be^^ . 

 Then (35) 9 (3^) become 



A(- I \ - |x2 +x3) > B[i^X- ^ \2]= (37) 



A(.3^ X- 1"^^^ + B [-|X - |X^ f X3] = 0. (38) 



Hence, since the determinant of these two simultaneous 

 equations must vanish, we have 



(x3-|x2-|x)2 + 22 (x-K^)" = 0, C39) 



Then, 



3+V^i '/3i^ 3 -V3±r -1/31^ 



1/3 2LI-L\ ■/3i^ ^ -/■^-V 



T 



V° = .S. -r r + A^e 2 ^+ Ape 4A,e 2 ^+ A^e + A;l 



1 ^ ^ 5 '^ 3 



,1/3 3+ '/II , \/3i?; >j5_J:r . \/3i^ 



V° = ii ::^^+B^e 2 ''+626 +B,e 2 +B,e +Bj_. 



1 3 V^ ^ ^ 



Hence, "rom (3^) 



V^^ = a COS.: sin nsy e "2/3 | eos(l5l) [-^^^ + A^e'/^i^^ A^e'^^^Aj 



\Al ^e^^^ - r ^^^ - ^''Si^ ,^ -V2 



+ sin (-^) [ .11-—-— f- ^ + B„e +B> e +B, ] f e "^^ 



2 3 \/3 ^ ^ -^ J 



(hi) 



