How to Tackle Differential Equations in Further Maths

Differential equations can be a challenging topic, but they are extremely rewarding once you understand them. My strategy is to first make sure that I am solid on the basics of calculus—especially differentiation and integration—because they are essential for solving these equations.

When dealing with first-order differential equations, focus on understanding how to separate variables and integrate both sides of the equation. For second-order differential equations, get comfortable with using characteristic equations and finding particular solutions. Make sure you understand the difference between homogeneous and non-homogeneous equations, as this will help you choose the correct method to solve them.

Practice is crucial. Working through different types of differential equations—from basic to more complex—will help you recognize patterns in how to solve them. I also found it helpful to study real-life applications of differential equations, such as population growth models or physical systems, to see the practical side of the mathematics.