function bvplinshoot
% BVPLINSHOOT  Implementation of the linear shooting method to
% solve problem 2(b) on Assignment #10.
% ELB 5/11/05

a=1;  b=-pi;  % boundary values
N=100; x=0:1/N:1;
% call ode45 with default tolerance to solve each IVP:
[xjunk,W1]=ode45(@ivpone,x,[1 0]');   % note xjunk=x
[xjunk,W2]=ode45(@ivptwo,x,[0 1]');
u1=W1(:,1)';  u2=W2(:,1)';

c1=1;  c2=(b-a*u1(end))/u2(end);
u=c1*u1+c2*u2;
plot(x,u,x,u1,'--',x,u2,':'),  xlabel x
legend('BVP solution u','soln u_1 to first IVP','soln u_2 to second IVP')

function dW=ivpone(x,W)
dW=[W(2);  -sin(x)*W(2)+5*W(1)+x^2-2];  % w nonhomogeneous term

function dW=ivptwo(x,W)
dW=[W(2);  -sin(x)*W(2)+5*W(1)];  % w/o nonhomogeneous term