$(15$ points$)$ Consider the following strong form:

$u(0)=1$

$u(1)=-2x-u_{,}-u+2x^2=0,in,(x),0$

subject $to$

$u(0)=1$

$u(1)=-2$

Derive the weak form $of$ this problem appropriate for a Galerkin discretization. Treat $$ and $as$ general

functions $ofx$ when constructing the weak form. $Be$ sure $to$ define the weighting and trial spaces.