Question: 14.2 (33 POINTS) A boundary value problem is defined by the following DE and boundary conditions. d2u x=sinpx, 0xl; u(x)=0,u(l)=0 dx2 l 1. (10 pts)

14.2 (33 POINTS) A boundary value problem is defined by the following DE and boundary conditions. d2u x=sinpx, 0xl; u(x)=0,u(l)=0 dx2 l 1. (10 pts) Solve the DE for an exact solution. 2. (18 pts) Assuming the approximating function is given by , Solve for an approximate solution using each of the following three methods: i. Collocation method ii. Method of least squares iii. Galerkin's method. 3. (5 pts) Compare the solutions to the exact solution graphically and by calculating the integral of the residuals over the range for the three MWR approximations

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