$($a$)$A simple supported beam is subjected to concentrated moments at both the ends.

$EI\frac{d^{2}y}{(d)x^2}-M_0=0,$ for xin$(0,l)$ with $y(0)=y(l)=0$

Solve using Galerkin method and compare with the exact solution. Consider:

$($i$)$ Trigonometric approximation with two terms.

$($ii$)$ Polynomial approximation with four terms.