The teaching of differential equations continues to pose a persistent challenge in engineering education, as many students master procedural steps mechanically without consolidating deep conceptual understanding. This study examines the impact of a generative AI tutor, Tu Tutor de Ecuaciones Diferenciales, integrated with Mathematica, on conceptual comprehension and problem-solving efficiency. A quasi-experimental design involved 135 students distributed in five groups: three experimental (n=83) and two control (n = 52). Experimental groups interacted with the AI tutor for step-by-step guidance, while control groups followed traditional instruction. Data collection combined entrance and exit surveys, performance tests, rubrics for mathematical justification, time tracking, and prompting analysis. Results show that experimental groups achieved significantly higher accuracy (82.4% vs. 74.1%), reduced solution times (18.6 vs. 24.4 minutes), and stronger justifications (M=4.1 vs. 3.3). Longitudinal analysis revealed a cumulative effect across the ten weeks, with widening performance gaps over time. Furthermore, prompting quality correlated strongly with reduced error (r=-0.58, p<0.001), positioning prompting as an emergent competency in AI-mediated mathematics education. These findings indicate that generative tutors, when responsibly integrated, not only improve efficiency but also foster higher-order engineering competencies such as critical decision-making and rigorous methodological implementation.
