Abstract A new method to solve the coupled two point kinetic model with a time varying reactivity for reflected reactors is presented using analytical method. The technique is based on an explicit analytical solution based on a set of basis functions in the form of exponential functions. This set of basis functions for the transient solution are developed by multiplying each term by the corresponding eigenvalues and eigenfunctions of the two-point kinetic matrix. The developed method was found to be very fast, accurate and has the ability to reproduce all the features of the transients including prompt jump; the stiffness of the equations is also overcome. The formulism is applicable equally well to a non-linear problems, where the reactivity depends on the neutron population through temperature feedback. It was evident that the presented method is proved to be an excellent solution for cases in which the reactivity is represented by a series of steps and improves accuracy and efficiency for more general cases of time varying reactivity and reactivity feedback.