Solutions of First-Order and Reducible Higher-Order Ordinary Differential Equations

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

Payment required for enrolment
Enrolment valid for 12 months

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

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

Chapter lessons

1.Directly-integrable equations13:26

Solving higher-order ODEs that are directly integrable.

2.Dependent variable absent23:03

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

3.Independent variable absent23:17

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

4.Worked examples (1)16:20

Worked examples on solving reducible higher-order ODEs.

5.Worked examples (2)53:20

More worked examples on solving reducible higher-order ODEs.

6.Worked examples (3)16:54

More worked examples on solving reducible higher-order ODEs.