Using the Galerkin method, solve the following differential equation with the approximate solution in the form of \(\tilde{u}(x)=c_{1} x+c_{2} x^{2}\). Compare the approximate solution with the exact one by plotting them on a graph. Also, compare the derivatives \(\mathrm{d} u / \mathrm{d} x\) and \(\mathrm{d} \tilde{u} / \mathrm{d} x\).

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