The basic differential equation of the elastic curve for a cantilever beam (Figure) is given as

El d2y/dx2 = -P(L - x)

where E = the modulus of elasticity and l = the moment of inertia. Solve for the deflection of the beam using a numerical method. The following parameter values apply: E = 30,000 ksi, l = 800 in4, P = 1 kip, L = l0 ft. Compare your numerical results to the analytical solution.

y = - PLx2/2El +Px3/6El