Solving First-order Linear ODE's; Steady-state and Transient Solutions

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Lesson Summary:

In this lesson, the focus is on solving first-order linear ODEs and understanding steady-state and transient solutions. The first-order linear ODE is a common model that occurs frequently in various applications and can always be solved. The lecture includes examples of two such models: the conduction model and diffusion model, which are both represented by the same equation with different variables. By the end of the lesson, students will learn the importance of the first-order linear equation and the standard form for solving it.

Lesson Description:

Solving First-order Linear ODE's; Steady-state and Transient Solutions -- Lecture 3. Learn how to solve most differential equations.

Arthur Mattuck, 18.03 Differential Equations, Spring 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), (Accessed November 26, 2008). License: Creative Commons BY-NC-SA.
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Questions answered by this video:
  • What is the first-order linear equation?
  • How do you solve differential equations?
  • What is a first-order linear ODE?
  • What is a transient solution?
  • What is a steady-state solution?
  • What is standard linear form?
  • What are real-world problems of differential equations?
  • Staff Review

    • Currently 4.0/5 Stars.
    In this video, you will learn the second-most important method of solving differential equations after separation of variables, the first-order linear equation. Some real-world differential equation problems are also discussed. A critical lesson to this course.