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

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
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.