% Section 4.5 Exercise 16
% y'' + 5*y' + 4*y = 4-t.^2
% with the 
% particular solution:
% yp=-1/6*t.^2+5/18*t+53/18
% and the 
% homogeneous solution:
% yh = c1*exp(-2*t) + c2*exp(-3*t) 
t = linspace(-1,10,100);
c1=1;c2=0.001;
yh = c1*exp(-2*t) + c2*exp(-3*t) ;
yp = -1/6*t.^2+5/18*t+53/18;
y = yh + yp;

figure(16)
plot(t,yh,'.-.r',t,yp,'-ob',t,y,'-g','Linewidth',2)
legend('homogeneous','particular','solution')
title('Again - notice the transient !!!')
