Скачать или смотреть Nonhomogeneous Linear Ordinary Differential Equations

In the previous video (   • Homogeneous Linear Ordinary Differential E...  ) we examined solving homogeneous linear ordinary differential equations (the forcing function was equal to 0). In this video we discuss how to solve nonhomogeneous linear ordinary differential equations which has the forcing function equal to a non-zero function. The approach outlined in this lecture is applicable to higher order ODEs but we focus on an example of

a*x’’(t) + b*x’(t) + c*x(t) = g(t)

with x(0) = x0 and x’(0) = xdot0

We leverage tactics developed in the previous video to solve the homogeneous portion of the solution. In this video, we use the Method of Underdetermined Coefficients to find the particular portion of the solution that corresponds to the forcing function. We then show how to choose coefficients of the solution to satisfy the initial conditions. This process is sometimes referred to as the traditional approach to solving linear ODEs. We compare and show how the Laplace technique yields the same solution.

Topics and timestamps:
0:00 – Introduction
6:04 – Theory of the total solution
20:36 – Building the total solution
30:05 – Method of Undetermined Coefficients
47:40 – Checking results using the Laplace Technique
53:07 – Example #2
1:07:24 – Summary

Lecture notes and code can be downloaded from https://github.com/clum/YouTube/tree/...

References:
-Introduction to Ordinary Differential Equations (coming soon…)
-Homogeneous Linear Ordinary Differential Equations (   • Homogeneous Linear Ordinary Differential E...  )
-The Laplace Transform (   • The Laplace Transform  )
-Partial Fraction Expansion/Decomposition (   • Partial Fraction Expansion/Decomposition  )
-The Inverse Laplace Transform (   • The Inverse Laplace Transform  )

All Ordinary Differential Equation videos in a single playlist (   • Ordinary Differential Equations  )

#ODEs

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