I have a partial differential equatons as shown below. $$\dfrac{d}{dx}((1+x)\dfrac{du(x)}{dx})=0$$ With the following boundary conditions. $$u(0)=0, u(3)=10$$ To solve it using FEM, I multiplied the PDE with residual function then converted it to its weak form.
Then constructed to global matrices using three elements within the global boundary.
Remember that, to solve the matrix system we need to solve following equation. $$[A][u]=[b]+[D]$$ $[D]$ corresponds to the matrix who includes the information about boundary conditions.
Since we do not have a constant on the right hand side on the first equation, we do not have the $[b]$ matrix.
I constructed $[D]$ matrix, as shown below. $$D=\left(\begin{array}{c}(1+x)B \\0 \\0 \\-(1+x)B\end{array}\right)$$
After this point what should I do? How should $1+x$ term affect the imposing Dirichlet BCs to this system?