clear 

%%
% Consider the linear BVP 
% u'' - cos(x) u' + sin(x) u = 0, 0 <= x <= pi/2, u(0)=1, u(pi/2)=e.
%
% Its exact solution:
exact = @(x) exp(sin(x));

%%
% The problem is presented in our standard form, so we can identify the
% coefficient functions in the ODE. Each should be coded so that they
% can accept either scalar or vector inputs.
p = @(x) -cos(x);
q = @(x) sin(x);
r = @(x) 0*x;      % vector!

%%
% We solve the BVP and compare the result to the exact solution.
[x, u] = bvplin(p, q, r, [0 pi/2], 1, exp(1), 25);

subplot(2, 1, 1)
plot(x, u, '.-')
ylabel('solution')
grid on
title('Solution of the BVP')

subplot(2, 1, 2)
plot(x, exact(x)-u, '.-')
ylabel('error')
grid on