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In order to solve differential equations, you will need to be really comfortable with performing integrals. These resources from Maths IA should help you revise.

These three PDF handouts are useful for doing different types of integration:

• Table of derivatives (PDF handout)  
• Useful trigonometric identities (PDF handout)  
• Techniques of integration (PDF handout)  

This PDF document contains many written worked examples of various techniques of integration.

• Techniques of integration worked examples (PDF booklet)  

This seminar was given in for Maths 1A Sem 1 2021 and covered the techniques of integration (substitution, by parts, trig substitution, partial fractions and upper and lower sums).

This seminar was given for Maths 1A in Sem 1 2014 and covered the entire of the techniques of integration topic. (Note that the seminar also includes reduction formulas and numerical integration, which are no longer in Maths 1A and you won't need for DEs for Engineers.)

You will occasionally need to do partial derivatives in this course. This Maths IB seminar from 2012 had a section about partial derivatives starting at 18m16s:

While solving systems of linear ODEs, you will need to find the eigenvalues and eigenvectors of matrices. These resources will help revise that process.

This PDF handout list various facts about eigenvalues and some examples of classic problems using them.

• Facts about eigenvalues handout 

This seminar from 2012 covers eigenvalues and eigenvectors for matrices (it was given for students in Maths 1A but this topic has now been moved to Maths 1B).

This seminar for Maths 1B from Summer Semester 2020 started with a section on eigenvectors.

A section of this course will use infinite series techniques to solve differential equations. These resources will help to revise the skills you need.

This seminar for Maths 1A Sem 1 2016 discussed how sum notation works, the rules for how it interacts with other operations, and some of the special manipulations you can do with it.

This seminar for Maths 1B in Summer Semester 2019 ended with a section on infinite series examples (starting at 1h30m), and it contains most of the skills you need for DEs.

This course begins where the differential equations content from Maths IB leaves off. These resources will help you revise the differential equations from Maths IB.

This seminar for Maths IB from 2014 covered various topics on differential equations, including first order separable equations, integrating factors, second order linear equations and the logistic equation. In this seminar, there was a Prezi presentation showing the process of solving linear second order differential equations. There is a link below to a PDF handout version.

• Second-order linear differential equations with constant coefficients handout  

This seminar for Maths IB from 2023 covered second order linear (constant coefficient) differential equations, including finding the general solution to homogeneous equations via the characteristic equation, and finding a particular solution to a non-homogeneous equation.

In this seminar for Maths IB from Semester 2 2018, the first part covered phase diagrams for differential equations. There was a Desmos graph that David showed in this seminar, which there is a link to below.