The basic differential equation of the elastic curve for a uniformly loaded beam (shown in Figure 4) is given as:
wLx - wx^2 EI dx^2 = 2
where E is the modulus of elasticity and I is the moment of inertia. Given the parameters E = 200,000 MPa, I = 3 x 10^-4 m^4, w = 15 kN/m, and L = 3m,
Solve for deflection using the shooting method (you can use ode45 to integrate), and compare against the analytical solution.
The analytical solution is:
wLx^3 - wx^4 + wL^3x / 12EI - 24E + 24EI
Please show how to solve this in Matlab.