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.

2

3 hrs

Payment required for enrolment
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.
[UI, Ibadan] MAT 241: Ordinary Differential Equations
[UI, Ibadan] MAT 241: Ordinary Differential Equations
Comprehensive treatise of advanced calculus covering ordinary differential equations, finite differences, difference equations and numerical integration. Curated for second-year students of engineering and physical sciences at University Of Ibadan, Nigeria. Students and professionals with a similar learning goal will also find this learning track useful.

Comprehensive treatise of advanced calculus covering ordinary differential equations, finite differences, difference equations and numerical integration. Curated for second-year students of engineering and physical sciences at University Of Ibadan, Nigeria. Students and professionals with a similar learning goal will also find this learning track useful.

Course Chapters

1. Introduction

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

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2. Separable Equations

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

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3. Homogeneous Equations

Meaning and solution of homogeneous first-order ODEs.

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4. Transformable Non-Homogeneous Equations

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

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5. Exact Equations

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

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6. Transformable Inexact Equations (1)

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

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7. Transformable Inexact Equations (2)

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

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8. Transformable Inexact Equations (3)

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

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9. Linear Equations

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

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10. Transformable Non-Linear Equations

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

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11. Variable-Solvable Equations

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

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12. Reducible Higher-Order ODEs
3
3

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

Chapter lessons

12-1. Directly-integrable equations
13:26

Solving higher-order ODEs that are directly integrable.

12-2. Dependent variable absent
23:03

Solving higher-order ODEs by reduction to lower-order ones when the dependent variable is absent.

12-3. Independent variable absent
23:17

Solving higher-order ODEs by reduction to lower-order ones when the independent variable is absent.