Solve the boundary value problem xy’’ +2y’ − xy = e_{x} 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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