The displacement of a simply supported beam subject to a uniform load is given by the solution of the following differential equation (for small displacements);

and q is the uniform load per unit length, L is the length of the beam, I is the moment of inertia of the section of the beam, and E is the modulus of elasticity. You are required to find the displacement y(x) using the following data:

For a rectangular beam: I = wh³ / 12 where w is the width of the beam and h is its height.

You should take: E = 200 GN/m², L =  5.0m w = 5.0 h = 10.0cm. Also, q = 1500.0  N / m on the 5.0 cm face.

Write a computer program to find y(x): (a) using the shooting method, and (b) using finite differences. Compare the results you obtain using both methods with respect to accuracy, computer runtime &c. Make sure you submit a report of your work in accordance with the instructions that appear on the course's site.