The one-dimensional nuclear reactor kinetics equation with feedback is solved by a perturbation method that gives asymptotically stable solutions for a step input of reactivity. The transient solutions are obtained by expanding each perturbation term in a series of spatial modes and applying Laplace transforms. It is shown that assuming the initial fuel temperature distribution is not equal to the coolant temperature distribution, the asymptotic flux depends on the initial state of the system if the harmonics are taken into account. This conclusion is further reinforced by analyzing the solution of the nonlinear spatial problem representing the final equilibrium state in terms of the solutions of the nonhomogeneous Mathieu equations.