If ar2 + br + c = 0 has equal roots r1, show that L[ert] = a(ert)" + b(crt)' + cert = a(r - r1 )2er1. Since the right side of is zero when r = r1, it follows that exp(r1,t) is a solution of L[y] = ay" + by' + cy = 0. Differentiate with respect to r and interchange differentiation with respect to r and with respect to t, thus showing that Since the right side of is zero when r = r1 conclude that t exp(r1 t) is also a solution of L[V] =0. Determine a suitable form of Y(t) if the method of undetermined coefficients is to be used. y" + 2y' + 5y = 3et-t cos2t - 2te-2t cost