In this lesson, learn how to solve linear ODEs with constant coefficients and understand what solution curves look like. The lecture covers the behavior of solutions and the use of complex methods to solve first-order linear equations. The steady state solution and transient solutions are explained, as well as the superposition principle for inputs. The lecture concludes by discussing how to solve differential equations when the physical input is trigonometric, using complex numbers to simplify the problem.
First-order Linear with Constant Coefficients: Behavior of Solutions, Use of Complex Methods -- Lecture 7. Learn how to solve linear ODEs and what solution curves look like.
Arthur Mattuck, 18.03 Differential Equations, Spring 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 26, 2008). License: Creative Commons BY-NC-SA.
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What is a first-order ODE with constant coefficients?
What is a steady-state solution?
What is a transient solution?
How do you solve a linear ODE?
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This video does some more to explain what solutions to linear ODEs look like, how to solve them using ordinary methods, and using complex methods to solve. This is another rather abstract lesson without actually solving an ODE.