In this PowerPoint, we explore the topic of “Differential equations”, namely the ones of 1st and 2nd order.
For the 1st case, we begin by revisiting the technique of “separating variables” and then explore how to use an integrating factor, showing the reasoning and providing examples for its application.
In the next section, we introduce 2nd order differential equations, with constant coefficients. All the steps to obtain a general solution are shown, including obtaining the general solution of the homogeneous equation associated, as well as the obtention of a particular solution. We also explain the usual techniques to calculate all the constants inherent to the process and show several examples related. Additionally, we provide a list of useful “changes of variable” to use for those equations with non-constant coefficients.
In the last section, as in previous resources for Pure Mathematics and Further Pure Mathematics, we include a series of solved exam-style questions, showing all the algebraic steps taken as well as tips and detailed explanations.
Hopefully, this resource can help students when revising for their examinations as well as teachers, who can use it a complement to their explanations in lessons.