I wrote this activity to help my students categorize the three kinds of separable differential equations: independent variable only; dependent variable only; both independent and dependent variables.
There are 12 cards. The first task is to look beyond all of the given information and verbiage and to look only at the DE and classify it as one of the three types. Once the students have classified, they check their results with the teacher and begin to answer the questions. Some involve solving the DE, some involve using it for other purposes.
There is an answer key included and more specific directions too. Several very smart people have given me feedback on this and we think we have fixed everything, but if you see a mistake, please let me know. You can email me at firstname.lastname@example.org