Assignment:
Use the Rayleigh-Ritz method to find two successive approximate solutions to the extremum problem associated with the functional.
using the trial function y0(x) = a3x3 + a2x2 + a1x + a0, where a0, a1, a2, and a3 are chosen so that Y0(x) satisfies the boundary conditions and Y1(x)=Y0(x)+c x2(1-x)2.
Provide complete and step by step solution for the question and show calculations and use formulas.