Abstract This research is an approach to the study of metaphors in the teaching of differential equations, present in textbooks. The objective is to analyse the cognitive metaphors that facilitate learning in the search for the solution of homogeneous linear differential equations. The methodology used was content analysis applied to a subjective sample of four university texts. The analysis allowed to find that the texts that use linear algebra make it easier the teaching of differential equations, and it is concluded that the metaphors from linear algebra are fundamentals in the teaching of linear differential equations, the basic concept facilitates the learning for the construction of the general solution of linear differential equations.