Answer Happy

Important!
I only need a Matlab solution for
this problem in other words solution to Problem
6. A Matlab solution in which
each line of code is explained through comments is required. The
analytical handwritten solution is available through
the following links. These are solutions to
the same question, with the only exception for one over the other
being that the first link has all parts solved.
https://www.answers.com/homework-help/que ... -q22117483
https://www.answers.com/homework-help/que ... -q20703207
Laplace Transform Solution of the Wave Equation Laplace transform can be used to solve certain partial differential equations. To illustrate this technique, consider the initial-boundary value problem azu azu 0<x<00, t>0, (a) at2 дх2? u(0,t) = h(t) t>0, (b) u(x,0) = 0, 0<x<0, (c) ди (x,0) = 0, 0<x<0, (d) at lim u(x, t) = 0, t20 (e) X-700 This problem arises in studying a semi-infinite string that is initially horizontal and at rest and where one end is being moved vertically. Let u(x, t) be the solution to (a)-(e). For each x, let 00 U(x,s) := L{u(x, t)} = = U8,9) = Lļu(x1) 1 ° e-stu(x, t) dt.

5. To Address - Laplace Transform Solution of the Wave Equation A. Using the fact that

a2 0x2 L{u}, (อน) L ax show that U(x,s) satisfies the equation a2u s2U(x,5) = a? 0<x<0. (f) дх? B. Show that the general solution to (f) is U(x,s) = A(s)e-sx/a + B(s)esx/a, where A(s) and B(s) are arbitrary functions of s. c. Since u(x, t) + ( as x + c for all 0 St<0, we have U(x, s) → 0 as x → 00. Use this fact to show that B(s) in part (B) must be zero. D. Use equation (b) to show that A(s) = H(s) = {{h}, where A(s) is given in part (B). E. Use the results of part (B), (C) and (D) to obtain a formal solution to (a)-(e). Compare it with solution obtained by the method of separation of variables.

After addressing the given scenario's analytically. You are required to: • Solve the problem using MATLAB. • Provide graphs of solutions from MATLAB on a single plot. • Compare your analytical and MATLAB solution. 6. Program Requirement On every run, the program must display name of your software house, and your team along with student ids. • At this stage, a message should be displayed to press any key to continue. • On press of a key, the program must ask the user whether they want to provide initial/boundary values, or the program should run with default values. Default values are provided in the problem statement. • After the input from user, the program must solve the problem and display the results. • At this stage, the program must ask the user if they wish to run another query or terminate the program. Based on user input, program must act accordingly.