In the name off ALLAH

Problem $3$

a$)$ Develop the weak form for the strong form:

$\frac{d^{2}u}{d{x}^2}+2sin(x)=0,u(0)=1,\frac{du}{dx}{|}_x|=\frac{}{2}=0$

b$)$ Obtain a solution to the developed weak form by using trial solutions and weight functions of the form:

$u(x)={}_0+{}_{1}x$

$w(x)={}_0+{}_{1}x$