7. Solve the differential equation in Problem 6 for the following boundary conditions using Galer¬

kin method:.

m(0) = 1, ii(l) = 2 Assume the approximate solution as u{x) = 0o (x) + C\

where 0o(x) is a function that satisfies the essential boundary conditions and

(j)\ (0) = 0i (1) = 0. Hence, assume the functions as follows:

Compare the approximate solution with the exact solution by plotting their graphs. The exact solution can be derived as m(x) = 2.9231 sinx + cosx — x