Solve the same problem as in example 2.1 using \(\tilde{u}(x)=c_{0}+c_{1} x+c_{2} x^{3}\).

Data From Example 2.1:

Calculate the approximate solution of eq. (2.1) using the weighted residual method. Use

(a) \(W(x)=1\) and

(b) \(W(x)=x\). Compare these solutions with the exact solution. Assume the approximate solution to be \(\tilde{u}(x)=c_{0}+c_{1} x+c_{2} x^{2}\) and \(p(x)=x\).

Equation 2.1:

du dr +p(x)=0, 0x1 u(0)=0 du dr (1)=1 Boundary conditions. (2.1)