When the solution of the following differential equation is approximated by \(\tilde{u}(x)=a_{0}+a_{1} x^{2}\), calculate the unknown coefficient(s) using the Galerkin method. Note that the approximate solution must satisfy the essential boundary conditions

Transcribed Image Text:

du dr +u=1, u(0)=0, du(1)/dx=0, 0x1.