Solve the boundary value problem xy’’ +2y’ − xy = ex given that y(0) =0.5 and y(2) = 3.694528, using the finite difference method implemented by the function two point. Use 10 divisions in the finite difference solution and plot the results, together with the exact solution, y=exp(x)/2. Determine the finite difference equivalence of the characteristic value problem defined by y + λy =0, where y(0)=0 and y(2)=0. Use 20 divisions in the finite difference method. Then solve the finite difference equations using the MATLAB function eig to determine the lowest value of λ, that is the lowest eigenvalue.

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