Current views on the teaching of differential equations (DEs) are shifting towards the use of graphical and numerical methods. Motivated by recent research suggesting that puzzle-based learning (PzBL) can improve the teaching and learning of STEM subjects and by the lack of relevant studies for DEs, we designed two tasks--sophism and paradox--to explore undergraduate engineering students' conceptual understanding of a classical topic--exact DEs--and to analyse the process of meaning-making during collaborative learning in small groups. One hundred and thirty-five undergraduate engineering students from a public university in Iran participated. In response to recent research signalling the tendency of the students to procedural learning of DEs, we analyse how the students in our study engaged in small group work on puzzle tasks, gaining a more conceptual understanding of exact DEs and acknowledging the efficiency of PzBL in their responses to a questionnaire and in interviews.