Is this what you want? Live script vesion is attached.
xmesh = linspace(0.01,0.05,5);
solinit = bvpinit(xmesh, @guess);
sol = bvp4c(@bvpfcn, @bcfcn, solinit);
plot(sol.x, sol.y, '-o')
function bound = bcfcn(ua,ub)
bound = [ua(1)-0.1, ub(1)];
end
function g = guess(r)
g = [1*(0.05-r)/(0.05-0.01), -1/(0.05-0.01)];
end
function dudr = bvpfcn(r,u)
dudr = [u(2), u(2)./r];
end
