This paper proposes an exponential interpolation to merge a part-of-speech-based language model and a word-based$n$-gram language model to accomplish word prediction tasks. In order to find a set of mathematical equations to properly describe the language modeling, a model based on partial differential equations is proposed. With the appropriate initial conditions, it was found an interpolation model similar to the traditional maximum entropy language model. Improvements in keystroke saved and perplexity over the word-based$n$-gram language model and two other traditional interpolation models is obtained, considering three different languages. The proposed interpolation model also provides additional improvement in hit rate parameter.