The cantilever beam shown below has length \"L\" and is subjected to a load P at

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The cantilever beam shown below has length "L" and is subjected to a load P at the end. The governing equation for the above problem is EI d2y/dx2 = M(x), where M(x) = P (L -x). Assume a polynomial solution in the form of y(x) = c0 + c1x+c2x2 + c3x3. Show that c0 and c1 have to be equal to zero based on the boundary conditions imposed. Use collocation method (put the collocation points at x = L/2 and x=L), subdomain method, least square method, and Galerkine's method to determine c2 and c3. Estimate the maximum deflection based on the four methods described in part (2).

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