Differential Equations Examples: Homogeneous Differential Equations

Описание: In this example problem video, we solve homogeneous differential equations step by step.
Homogeneous differential equations can be solved by making an appropriate change of variables, typically using y = u x or x = v y, which reduces the equation to a separable differential equation.

In this video, you’ll see examples involving:
• Identifying homogeneous differential equations
• Choosing an appropriate substitution
• Reducing the equation to separable form
• Solving the resulting equation
• Initial value problems

These worked examples are designed to help you recognize homogeneous equations and apply the substitution method accurately and confidently.

This video is part of my Differential Equations examples series.

Differential Equations playlist:
   • Ordinary Differential Equations | Complete...  

Guided notes and additional resources:
https://www.understandthemath.com

ODE Videos
   • Ordinary Differential Equations Free Cours...  
   • Classification of Differential Equations |...  
   • Slope Fields for First-Order Differential ...  
   • Autonomous Differential Equations | Critic...  
   • Separable Differential Equations | Definit...  
   • Linear Differential Equations | Integratin...  
   • Exact Differential Equations | Definition,...  
   • Homogeneous Differential Equations | Defin...  
   • Bernoulli Differential Equations | Method,...  
   • Applications of First-Order Linear Differe...  
   • Euler’s Method | Numerical Approximation f...  
https://youtu.be/xhW_XmerR94/ordinary...

Timestamps
00:00 Steps and General Forms
00:23 Example 1
06:38 Example 2

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More About Understand The Math
Understand The Math offers clear, accessible, and engaging mathematics instruction for students and lifelong learners. I'm Cheryl Hile, the founder of Understand The Math, with a Ph.D. in Engineering Science and Applied Mathematics and over 25 years of university teaching experience. My goal is to provide accurate, high-quality math instruction through step-by-step explanations and carefully worked-out examples.

Each video includes free guided notes, linked in the description. These notes help students follow along, highlight key concepts, and practice problems, making review easier and more effective.

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