An ODE (ordinary differential equations) model of bubble dynamics is described in details. An ODE model is sometimes superior to a PDE (partial differential equations) model such as computational fluid dynamics (CFD) in that it is computationally more economical and that the important factors are more easily traced. However, an ODE model needs to be validated by comparing with the experimental results. In an ODE model, temperature and pressure inside a bubble are assumed to be spatially uniform except at the thermal boundary layer near the bubble wall. Fictitious temperature jump at the bubble wall is assumed to calculate the heat flow across the bubble wall. Temporal variation of the liquid temperature at the bubble wall is crudely calculated using an ODE model. The temperature inside a bubble is calculated by the thermal energy of a bubble which change with time by pV work done on a bubble, thermal conduction across the bubble wall, heat exchange due to non-equilibrium evaporation or condensation of water vapor at the bubble wall, heat of non-equilibrium chemical reactions, etc. The number of water vapor molecules inside a bubble changes with time by non-equilibrium evaporation or condensation. Through the numerical calculations of rates of non-equilibrium chemical reactions inside a bubble, amounts of chemical products created inside a bubble are obtained. It is possible to numerically calculate the rates of dissolution of each chemical product into the surrounding liquid from the interior of a bubble through which an ODE model could be validated by the direct comparison with the experimental data. The derivations of Rayleigh-Plesset equation and Keller equation for bubble pulsation under ultrasound are also described.