%% E3_10
%% Carol Lucas
%% An analytical solution of the answer students are to get diagramatically.
%%    State 4,5 is considered to be 4.

mess='Program pauses between each major calculation.  Hit return to continue'

format compact

syms k12 k21 k16 k61 k46 k64 k43 k34 k32 k23 k24 k42
R1=[-k12-k16-k61 k21-k61 -k61 -k61];
R2=[k12 -k21-k24-k23 k32 k42];
R3=[0 k23 -k32-k34 k43];
R4=[-k64 k24-k64 k34-k64 -k42-k43-k46-k64];

A=[R1;R2;R3;R4];

b=[k61;0;0;k64];

x=-inv(A)*b;

x1=x(1);

mess=' SS for State 1: '
mess=' Note:  State 4,5 = 4'
pretty(expand(x1)),pause;

x2=x(2);

mess=' SS for State 2'
pretty(expand(x2)),pause;

mess=' SS for J12'
J12=-k12*x(1)+k21*x2;
pretty(expand(J12)),pause;

mess=' SS for x3'
x3=x(3);
pretty(expand(x3)),pause

mess=' SS for x4'
x4=x(4);
pretty(expand(x4)),pause;

mess='  SS for J32'
J32=-k32*x3+k23*x2;
pretty(expand(J32)),pause;

mess='  SS for J34'
J34=-k34*x3+k43*x4;
pretty(expand(J34)),pause;

mess=' SS for x6'
x6=1-x(1)-x(2)-x(3)-x(4);
x61=simplify(x6);
pretty(expand(x61)),pause;

mess='  SS for J46'
J46=-k46*x4+k64*x61;
pretty(expand(J46)),pause;