For the course notes, you may seek out this MEGA folder which contains all the exercises and notes. (Note : Delay differential equations has been added, with a lot of extra details than I taught in class).
Basic Idea and details of the course
This course was a 10.5 hour introductory course to differential equations for students of grade 11 and 12. However, the plan was slightly different : instead of going into a rigorous treatment of differential equations, we decided to go for studying different kinds of ansatz and how they can be used to solve simple differential equations. The plan, of course, was that if we went fast enough, we could see how ansatz actually help even when the underlying differential equation wasn't solvable - eventually leading up to Frobenius and power series. This treatment was fully rigorous, and while it can be dismissed as educated guessing, let us not forget that much more advanced DEs (for instance, stochastic DEs and iterated DEs) are indeed mostly solved using clever ansatz initially, before we get to the theory of existence and uniqueness. Of course we never went that fast, but we did well!
We began with the power and exponential ansatz. These were then generalized to the ansatz which can be used to solve linear differential equations. After this, we discussed ansatz for variable-separable differential equations. This was followed by second-order linear differential equations, and the Bernoulli differential equations. Examples (Population growth, Radioactive decay, Population growth with rate restriction, First-order chemical kinetics, Verhulst Model, Solow-Swan model) were used when needed.
A final surprise class (to be fair, that I would ever discuss this would take anybody by surprise) was taken on DELAY differential equations. Yes, you heard that right. We discussed the basic sine-ansatz for this, although the exponential ansatz is included in the notes.