first order linear differential equation (Nagle hw sol sect 2.3#9) | Summary and Q&A

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January 3, 2017
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first order linear differential equation (Nagle hw sol sect 2.3#9)

TL;DR

Learn how to solve a non-standard linear differential equation by finding the integrating factor and integrating both sides.

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Key Insights

  • 💁 Dividing the non-standard linear differential equation by X is the first step to transform it into a standard form.
  • 🥡 The integrating factor is determined by taking the integral of the X term's coefficient.
  • 🙃 Multiplying both sides by the integrating factor simplifies the equation and allows for easier integration.
  • 🍉 The solution includes a constant term to represent the general solution of the original differential equation.

Transcript

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Questions & Answers

Q: What is the first step in solving the non-standard linear differential equation?

The first step is to divide the equation by X to eliminate the X term in the coefficient.

Q: How is the integrating factor determined?

The integrating factor is found by taking the integral of the coefficient of the X term, in this case, 2/X.

Q: What is the purpose of multiplying both sides by the integrating factor?

Multiplying both sides by the integrating factor creates a product rule on the left-hand side and simplifies the equation.

Q: Why is there a constant term in the solution?

The constant term, denoted as C, is included in the solution because it accounts for the general solution of the original differential equation.

Summary & Key Takeaways

  • The video teaches how to solve a non-standard linear differential equation by dividing by X and rearranging the equation to a standard form.

  • The integrating factor is found by taking the integral of the coefficient of the X term.

  • Multiply both sides of the equation by the integrating factor and simplify to solve for the Y function.

  • The solution includes a constant term that needs to be determined through further calculations.

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