The rigorous three-point nodal equations in plane geometry derived in an earlier paper on the basis of invariant imbedding theory have been written in a continuous form by passing to the limit of zero node size. It has been shown that the obtained second-order differential equation is equivalent to the sec-ond-order integrodifferential Boltzmann equation or the diffusion equation, depending on the approximation used in the calculation of response functions entering the nodal equations.