%% PROBLEM 6_2 ALL MATLAB
function [t,xs]=P6_2(alpha,init,I1,I2)

gm=.05;cm=1;gc=.1;

A1=[-(gm+alpha*gc)/cm alpha*gc/cm];
A2=[gc/cm  -(gm+gc)/cm];
A=[A1;A2];
F=[I1/cm;I2/cm];

ss=-inv(A)*F;
ssv=[ss;[0;0]];

lam=eig(A)
dt0=A*init+F;

M=[1 1 0 0;0 0 1 1; lam.' 0 0; 0 0 lam.'];  %% Want non conjugate transpose
b=[init; dt0];
as=inv(M)*(b-ssv)

t=[0:.1:200];
x=as(1)*exp(lam(1)*t)+as(2)*exp(lam(2)*t)+ss(1,1);
y=as(3)*exp(lam(1)*t)+as(4)*exp(lam(2)*t)+ss(2,1);



[t,xs]=ode45('P6_2fun',t,init,[],alpha,I1,I2);
v1=xs(:,1);
v2=xs(:,2);


figure(1); clf;plot(t,x,t,y,t,v1,t, v2);xlabel('time (secs)');
title('Comparison of simulation and analytical solution');
mess='Hit return to continue.'
pause;