In the paper by \textit{D. Duffie} and \textit{R. Kan} [Math. Finance 6, No. 4, 379-406 (1996; Zbl 0915.90014)] it is shown that the short rate dynamics must be of linear/Gaussian or square root/affine form if the corresponding zero coupon bond price is exponential affine and the bond price is exponential affine if some Riccati equations have solutions. Stochastic flows and their Jacobians are used to show that the bond price is an exponential affine function if the short rate process is described by Gaussian dynamics as in the Vasilek model [\textit{O. Vasilek}, J. Finance Econ. 5, 177-188 (1977)] or the Hull-White model [\textit{J. Hull} and \textit{A. White}, J. Derivatives 2, 37-48 (1994)] or square root Bessel process as in the Cox-Ingersoll-Ross model [\textit{J. C. Cox, J. E. Ingersoll jun.} and \textit{S. A. Ross}, Econometrica 53, 363-384 (1985; Zbl 0576.90006)]. With the help of the forward measure the bond price is obtained by the solution of a linear ordinary differential equation.