The PowerPoint below provides an overview of material in this topic, including explanations and examples - for the full experience, open in a new tab then download it. All exercise references are to the new specification Pearson textbook - you can access the digital version for free or buy your own for extra practice.
Written summary notes are also given below for quick revision of key points, plus a selection of exam-style questions (with solutions) to test your understanding.
Section 1 Notes - 1st order DEs: Nearer Maths review
Section 2 Notes - 1st order DEs: Integrating factors
Section 3 Notes - 2nd order DEs: Auxiliary equations, SHM and damped oscillations
Section 4 Notes - 2nd order DEs: Complementary functions and particular integrals
Section 5 Notes - 2nd order DEs: Simultaneous DEs
Topic assessment 1 (with solutions) - 1st order DEs
Topic assessment 2 (with solutions) - 2nd order DEs
Use the videos below to support your understanding of the topic. The ones on the left are specific to the course, building up to demos of exam-style questions; the ones on the right are for your own amusement, although the alternative outlook may provide you with a deeper overall understanding and appreciation of the topic.
Topic videos:
Extra fun! Differential equations are ridiculously important in higher level mathematics and science. So you get a full playlist of lovely extension material: