Generalization of the analytical solution of neutron point kinetics equations with time-dependent external source

Point reactor kinetics equations with one groupof delayed neutrons in the presence of the time-dependentexternal neutron source are solved analytically during thestart-up of a nuclear reactor. Our model incorporates therandom nature of the source and linear reactivity variation.We establish a general relationship between the expectationvalues of source intensity and the expectation values ofneutron density of the sub-critical reactor by ignoring theterm of the second derivative for neutron density in neutronpoint kinetics equations. The results of the analyticalsolution are in good agreement with the results obtainedwith numerical solution.