Please solve using Matlab

Part A is solved analytic solution by hand

Part b Matlab Code Please explain what the code does with comments where neccessary

Note: Uses of Matlab built-in functions for solving ODEs, such as ode23 and ode45, are NOT allowed

Consider the following initial value problem for u(x) dened on x 2 0, u""u"'7u"+u'+6u=0, ("prime"isthederivative,d/dx) u(0)= 1.1, u'(0)=4.7, u"(0)=7.9, u"'(0)= 14.3. (a) Find the analytic solution, which will be used to validate the numerical solutions. (b) Solve the initial value problem by rst converting the original system into a system of rst-order ODEs, then solving the latter using the following three methods ("Ax" is "h" in the textbook): (I) Euler's explicit method, with Ax = 0.1 (II) Euler's explicit method, with Ax = 0.03 (111) Mid-point method, with Ax = 0.1 In all 3 cases, numerically integrate the system to x = 1.5 to nd the solution over the interval of 0 S x S 1.5. Plot the analytic solution and the numerical solutions using methods (I), (II), and (III) over the interval of 0 S x S 1.5. Collect all four curves in one plot and clearly label the curves. Note: For both Task 1 and 2, the numerical solutions are the main deliverables. An incorrect or missing analytic solution will be assessed a relatively minor deduction (~ 0.5 point)