"(My Code is correct)"
To me it's not. See below for the correction (the problem is I can't see it's change the solution after fixing the code, and I don't know why and did not investigated further for reason).
I give you here the code corrected + 2 methods to computs dy/dx
x1=0.06; x2=0.08;
xmesh = linspace(x1,x2);
solinit = bvpinit(xmesh, @guess);
sol= bvp5c( @heatcylinder1D, @bcfcn, solinit);
figure
hold on
plot(gradient(sol.y(1,:),sol.x),'ro-')
plot(deval(sol,sol.x,2)./sol.x,'b+-')
legend('dy/dx gradient','dy/dx deval')
function res = bcfcn(ya,yb)
res = [ya(1)-150
yb(1)-60];
end
function g = guess(x)
g = [1 1000];
end
function dxdy = heatcylinder1D(x,y)
dxdy = zeros(2,1);
dxdy(1) = y(2)/x;
dxdy(2) = 10*x; % <= error is here
end
