Solutions of First-Order and Reducible Higher-Order Ordinary Differential Equations - Mathematical Methods (Undergraduate Advanced)

This course breaks down the key types of first-order ordinary differential equations (ODEs) — separable, homogeneous, exact, linear, and more — plus how to handle tricky non-homogeneous and inexact ones by transformations. You’ll also learn how to reduce certain higher-order equations into first-order ones you already know how to solve. The course is straight to the point, method-focused, and designed to build your confidence with step-by-step explanations and examples. If you're a science, engineering, or math student or professional who wants clarity without fluff, this is for you.

3 hrs

Enrolment valid for 12 months

This course is also part of the following learning track. You may join the track to gain comprehensive knowledge across related courses.

MTH 202: Elementary Differential Equations

Mastering differential equations is essential for modelling dynamic systems in science and engineering. This learning track delivers the complete MTH 202 curriculum based on NUC CCMAS standards, equipping you with the mathematical command to describe motion, analyse electrical circuits, and predict rates of change across physical phenomena. This programme is targeted at undergraduates in mathematics, physics, engineering, and chemistry who possess a strong background in single and multivariable calculus. It also serves professionals requiring a rigorous, method-focused refresher on fundamental mathematical modelling tools. You will achieve competence in classifying equations and deploying solution methods for first-order, reducible higher-order, and general linear ordinary differential equations. You will learn to solve systems of linear ODEs and apply these techniques directly to real-world physical and technical problems. Completion establishes the necessary foundation for advanced studies in partial differential equations, control theory, and advanced physics.

Course Chapters

1. Introduction

A review of the fundamental concepts of differential equations and an introduction to first-order ordinary differential equations.

2. Separable Equations

Identification and solution of first-order ODEs solvable by separation of the dependent and independent variables.

3. Homogeneous Equations

Meaning and solution of homogeneous first-order ODEs.

4. Transformable Non-Homogeneous Equations

Identifying and solving non-homogeneous first-order ODES transformable to homogeneous and / or separable ones.

5. Exact Equations

Meaning and solution of exact first-order ordinary differential equations.

6. Transformable Inexact Equations (1)

Integrating factors and their use in transforming inexact first-order ODEs into exact ones - special cases.

7. Transformable Inexact Equations (2)

Integrating factors and their use in transforming inexact first-order ODEs into exact ones - by inspection method.

8. Transformable Inexact Equations (3)

Integrating factors and their use in transforming inexact first-order ODEs into exact ones - use of groups.

9. Linear Equations

Meaning, identification and solution of linear first-order ODES.

10. Transformable Non-Linear Equations

Identifying and solving non-linear first-order ODEs transformable to linear ones - Bernoulli and Riccati equations.

11. Variable-Solvable Equations

Identifying and solving first-order ODEs solvable for the dependent or independent variable.

12. Reducible Higher-Order ODEs

Identifying and solving higher-order ODEs reducible to first-order ones - when either the dependent or the independent variable is absent.

Concept Overviews

3 Lessons

59:46

Problem Walkthroughs

3 Lessons

1:26:34