Worked example: identifying separable equations | AP Calculus AB | Khan Academy

TL;DR

This video explains how to determine if a given differential equation is separable and provides examples for practice.

Transcript

• [Sal] Which of the differential equations are separable? And I encourage you to pause this video and see which of these are actually separable. Now, the way that I approach this is I try to solve for the derivative, and if when I solve for the derivative, if I get dy, dx is equal to some function of y times some other function of x then I say oka... Read More

Key Insights

• ☑️ Separable differential equations can be identified by solving for the derivative and checking for a product of functions of x and y.
• ☺️ Non-separable differential equations cannot be written in the form of a product of a function of x and a function of y.
• 🙃 Integrating separable differential equations involves dividing both sides, multiplying by dx, and integrating separately.

Questions & Answers

Q: How can you determine if a given differential equation is separable?

To determine if a differential equation is separable, solve for the derivative and check if it can be written as the product of a function of x and a function of y.

Q: What happens when a differential equation is separable?

When a differential equation is separable, it can be rewritten in a form where the product of a function of y and a function of x is equal to the derivative of y with respect to x.

Q: How do you integrate a separable differential equation?

To integrate a separable differential equation, divide both sides by the function of y, multiply both sides by dx, and integrate both sides separately.

Q: Can you provide an example of a separable differential equation?

One example of a separable differential equation is dy/dx = (1/y^2 + y)dx, where the equation can be rewritten as (1/y^2 + y)dy = dx.

Summary & Key Takeaways

• The video explores the concept of separable differential equations.

• Separable differential equations can be solved by rewriting them as a product of a function of x and a function of y.

• Examples are shown to differentiate between separable and non-separable differential equations.