R has mostly been used and applied for statistical computing and representation of graphs. But in the recent years it is quickly becoming more fitting for mathematical analysis and computing. Solving differential equations is one of the areas where R has made considerable advancement in. The project was aimed at finding out the application of R packages in differential equations. The statistical software is crucial in differential equations. Several R libraries have been developed to be used in solving differential equations. These libraries are known as R packages. Three main libraries have been considered briefly in this study. They include: deSolve, deTestSet and bvpSolve. The project sought to use the R libraries to solve mathematical models involving an equation in which a function and its derivative play an important role. Here, we give a detailed overview of how different types of differential equations can be solved using the different R packages. We describe three models; SIR model, logistic growth model and the pharmacokinetics model, and the role several of R packages in simulating their solutions which are applied in various practical situations.