The equations for a point kinetics model with a startup source are
$$\frac{dP}{dt}=\frac{\rho_{tot}-\bar{\beta}}{A}\times P+\sum^6_{i=1}\lambda_iY_i+S_0$$
$$\frac{dY_i}{dt}=\frac{\beta_i}{A}\times Q_{fis}-\lambda_iY_i$$
Where \(P\) is the reactor power, \(Y\) are the delayed neutron precursors, and \(S_0\) is the initial startup source.
Sources
el-genkPhysicsbasedDynamicModel