The paper presents results of two case studies with undergraduate students majoring in applied mathematics and engineering. The first case study deals with students’ preferences and difficulties with application problems and pure mathematics questions in their courses. The students were taking a second year course on ordinary differential equations (ODE). The students were asked about their preferences in dealing with application problems and pure mathematics questions and their difficulties with solving application problems not only in the ODE course but also in other courses. The second case study deals with students’ preferences for application problems and pure mathematics questions in their first and second year engineering mathematics courses. The students were majoring in engineering. Students’ responses are presented and discussed in the paper.