(Solved): [3] Use Galerkin method to formulate the generalized stiffness matrix and load vector for the oned ...

[3] Use Galerkin method to formulate the generalized stiffness matrix and load vector for the onedimensional ordinary differential equation $\frac{d^{2}u}{d{x}^2}=?u??$ where $0?x?1$. The boundary conditions involve either specifying $u$ or $du/dx$ at the end points of the one-dimensional element. Assume an approximation function in the following form: $u(x)=N_i(x)u_i,i=1,2\text{ and }{N}_i\left(x_j\right)={?}_{ij}$