Report no. 2 Applied Mathematics - laboratory 8) For a second order ordinary differential equation: y" + 4y' + 5y = 0 find the analytical solution y(x) for the boundary value problem: y'(0) = 0 {y(1) = e-² (2 sin(1) + cos(1)) Then create sets of algebraic equations using second order differential schemes for the first and second derivative for nodes N = 6 and N = 11 on the interval [0, 1] and solve them numerically using Matlab/Octave. Compare local errors in individual nodes (i.e. the difference between the numerical and analytical solution). On their basis, estimate the order of the method.