Differential equations is a branch of mathematics which is closely related to mathematical modeling that arises in real-world problems. Problem solving ability is an essential component to solve contextual problem of differential equations properly. The purposes of this study are to describe contextual teaching and learning (CTL) model in differential equations course, to improve lecturers' abilities in implementing CTL, and to improve students' problem solving ability in differential equations. The study was conducted in the fifth semester of 2015/2016 academic year with 34 students of mathematics education Universitas Muhammadiyah Surakarta as participants. The CTL model was applied by lesson study approach which involved three stages namely plan, do, and see in each cycle. This research was conducted in four cycles. The study results found that discovery-based CTL could be applied in differential equations course. The lecturer abilities to design discovery-based contextual learning plan, to present real-world problem in learning process, to design learning strategy and assessment instruments of problem solving improved significantly. Problem solving ability of students also improved during teaching and learning process. A bibliography is included.