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Problem El: Consider the general linear1 second order1 homogeneous constant coefcient IVP given by as + by' + cs = D shin} = an r'w)

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Problem El: Consider the general linear1 second order1 homogeneous constant coefcient IVP given by as\" + by' + cs = D shin} = an r'w) = a\": [a] Show that if the characteristic polynomial gives two complex roots1 then the solutions corresponding to those roots will form a fundamental set of solutions. [h] Now suppose the characteristic polynomial has a repeated root. Show that the solution corresponding to the repeated root does NOT form a fundamental solution set. [c] If we include the solution we obtained from reduction of order with this repeated root solution1 show that they do form a fundamental set of solutions

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