Cauchy - Euler Equations (Differential Equations)

Cauchy - Euler equations are the first type of second order ODEs with non-constant coefficients that we'll learn about. We go over how to convert to the auxiliary equation, the three different types of solutions, show the similarities to second order ODEs with constant coefficients, and how to make sense of x raised to a complex power. Problems are linked below.
Cauchy - Euler Equations Problem 1: • Cauchy - Euler Equatio...
Cauchy - Euler Equations Problem 2: • Cauchy - Euler Equatio...
Cauchy - Euler Equations Problem 3: • Cauchy - Euler Equatio...
Cauchy - Euler Equations Problem 4: • Cauchy - Euler Equatio...
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Music By: "After The Fall"
Track Name: "Pieces"
Music Published by: Chill Out Records LLC
License: Creative Commons Attribution 4.0 International (CC BY - 4.0)
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[@Nana-Danso]

Great work! Easy to understand

[@gentlemandude1]

Beautiful explanation. Love the side-by-side symmetric demonstration. However, it would be nice to see how reduction of order is used to get those natural logs in the solution set.

[@BlackTshirtMathProfessor]

Thank you. I left the proof as an exercise for the viewer 😁

[@gentlemandude1]

@@BlackTshirtMathProfessor Yes, what every math student loooves to hear from an instructor.🙎‍♂

[@BlackTshirtMathProfessor]

Send me an email and I’ll write you the proof for you

[@gentlemandude1]

@@BlackTshirtMathProfessor That is very generous of you, but I found the proof elsewhere. It is not as straightforward as I would have thought but it's comprehensible. Thanks for your offer!

[@strekoohi]

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[@webibekela9481]

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