% matlab script to illustrate uniqueness of BVP solution
% see Ascher and Petzold p4

close all, clear all

t0 = 0; tf = 3.5; dt = 0.1;
t = [t0:dt:tf];

u0    = 1;

for uDot0 = [0:0.25:1],
  alpha = sqrt(u0^2+uDot0^2);
  beta  = asin(u0/alpha);
  u = alpha*sin(t+beta);
  hold on
  plot(t,u)
end