In two previous studies we investigated the non-routine problem-solving abilities of students just finishing their first year of a traditionally taught calculus sequence. This paper reports on a similar study, using the same non-routine first-year differential calculus problems, with students who had completed one and one-half years of traditional calculus and were in the midst of an ordinary differential equations course. More than half of these students were unable to solve even one problem and more than a third made no substantial progress toward any solution. A routine test of associated algebra and calculus skills indicated that many of the students were familiar with the key calculus concepts for solving these non-routine problems; nonetheless, students often used sophisticated algebraic methods rather than calculus in approaching the non-routine problems. We suggest a possible explanation for this phenomenon and discuss its importance for teaching. (Contains 5 footnotes, 3 figures, and 6 tables.) [Partial support for this research was provided by the Exxon Education Foundation.]