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Introduction to first differential equations

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20 pages
2026/2027 Written for academic year
Institution University Of Johannesburg (UJ)
Course Introduction to differential equations (EMA206B)
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This document walks you through differential calculus methods. It also consists of examples and exercises with answers.

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Evaluation:
uaon :
1. Determine the order and the degree of a given
differential equation

2. Differentiate between linear and non-linear DE’s

3. Verify if a given function is a solution to a given
differential equation

4. Explain in your own words what is meant by
mathematical modelling



1

, What is a Differential Equation?
• Equation that contain derivatives
• Determines the relationship between a function and some of
its derivatives
• Represents dynamic relationships - quantities that change
• Examples:
dy
3  x  cos y
dx

d 2 y dy
3 2   x  cos y
dx dx

, TYPE:
Partial- / Ordinary Differential Equation?


• Ordinary differential Equation (ODE)
d 2 y dy
3 2   x  cos y
– Contain ordinary derivatives - dx dx

• Partial Differential Equation (PDE)
 2 
3 2   v  cos 
– Contain partial derivatives v v

– Significant differences in methods & techniques

Document information

Uploaded on
August 14, 2026
Number of pages
20
Written in
2026/2027
Type
Class notes
Professor(s)
P dhlamini
Contains
All classes
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R75,33
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