2. Solving the system of ordinary linear differential equations subject 

 to the boundary conditions yields 



q.x 



yi = 



ol .2 o2 1 



o 



1 + v 



1 q,s 



x < 



(D7) 



i , - * a „ -q. 6x 



ol .2 o2 1 

 6 e 



J 2 



1 + 



1 QiS 



x > 



(D8) 



3. The inverse transforms of Equations D7 and D8 are (Appendix A): 



6a. - a „ 

 ol o2 



'l " &(& + 1) 



'e. t -x Ae. t 



+ x erfc 



2/e.t 



(D9) 



x < 



Vo " 



6 a -a 

 ol o2 



2 6(6 + 1) 



*2 2/. 



■ t -6 x Me t 



- 6x erfc 



6x 



2/e t 



(D10) 



x > 



D2 



