162Economic Dynamics4.6 Solutions with repeating rootsIn chapter 2 we usedceλtandcteλtfor a repeated root. Ifλ=rwhich is a repeated root, then either there are twoindependent eigenvectorsv1andv2which will lead to the general solutionx=c1ertv1+c2ertv2or else there is onlyoneassociated eigenvector, sayv. In this latter case we usethe resultx=c1ertv1+c2(erttv+ertv2)(4.23)In this latter case the second solution satisFeserttv+ertv2and is combined withthe solutionertv1to obtain the general solution (see Boyce and DiPrima 1997,pp. 390–6). We shall consider two examples, the Frst with a repeating root, butwith two linearly independent eigenvectors, and a second with a repeating root but
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