Exact Differential Equation, (2.4#11) | Summary and Q&A

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January 10, 2017
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blackpenredpen
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Exact Differential Equation, (2.4#11)

TL;DR

The video explains how to determine if a given equation is exact, and if so, how to solve it using integration.

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Questions & Answers

Q: What is an exact equation in differential calculus?

In differential calculus, an exact equation is one where the equation can be written as the total derivative of a single function. It is determined by checking if the partial derivatives of the equation match the mixed partial derivatives.

Q: How do you check if an equation is exact?

To check if an equation is exact, you need to take partial derivatives with respect to each variable and compare the mixed partial derivatives. If they are equal, the equation is exact.

Q: What is the next step after determining an equation is exact?

Once an equation is determined to be exact, it can be solved by integrating the equation with respect to each variable separately. This will result in a function that includes constant terms.

Q: What is the purpose of the constant term in the solution?

The constant term in the solution accounts for the fact that the original equation could have multiple solutions. The constant allows for different solutions to be represented within a single function.

Summary & Key Takeaways

  • The video introduces the concept of an exact equation in differential calculus and explains the steps to check if an equation is exact.

  • The process involves taking partial derivatives with respect to each variable and checking if the mixed partial derivatives are equal.

  • If the equation is exact, the video demonstrates how to find the solution by integrating the equation with respect to each variable and adding a constant term.

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