Differential Equations Examples: Bernoulli Differential Equations

Описание: In this example problem video, we solve Bernoulli differential equations step by step.

Bernoulli differential equations can be transformed into linear first-order differential equations by using an appropriate substitution. Once rewritten in linear form, the equation can be solved using the integrating factor method.

In this video, you’ll see examples involving:
• Writing a Bernoulli equation in standard form
• Identifying the value of n
• Using the substitution u = y^(1 - n)
• Solving the resulting linear differential equation
• Converting back to the original variable

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

This video is part of my Differential Equations examples series.

Differential Equations playlists:
   / @understandthemath  

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...  
   • Differential Equations Exam Review | Class...  

Timestamps
00:00 Examples Introduction
00:17 Example 1
06:57 Example 2

In this example problem video, we model population growth with harvesting using differential equations.

We set up a differential equation that accounts for both natural population growth and a constant harvesting rate. After solving the equation, we analyze the long-term behavior of the population to determine what happens over time.

In this video, you’ll see examples involving:
• Setting up a population model with harvesting
• Writing and solving a linear differential equation
• Applying an initial condition
• Finding equilibrium solutions
• Interpreting the long-term behavior of the population

These worked examples show how differential equations are used to model real-world population dynamics.

This video is part of my Differential Equations application examples series.

Differential Equations playlists:
   / @understandthemath  

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...  
   • Differential Equations Exam Review | Class...  

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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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