Quick Differential Equations Question

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Homework Help Overview

The discussion revolves around a differential equation of the form xy'' + y' = 0, with participants exploring methods of solving it, particularly in the context of Cauchy-Euler equations.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the validity of multiplying the equation by x to transform it into a Cauchy-Euler form. Some suggest alternative methods, such as substituting w = y' and using an integrating factor. There is also a debate regarding the linearity of the equation.

Discussion Status

The discussion is active, with various approaches being considered. Some participants provide guidance on the multiplication method, while others raise questions about the nature of the equation and its classification.

Contextual Notes

Participants reference the Cauchy-Euler section of a textbook, indicating that the context of the problem is influenced by educational materials and their definitions.

jofree87
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xy'' + y' = 0

Is it ok to multiply this whole equation by x to make it a cauchy-euler equation?
 
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Why not just put w=y' and then solve using an integrating factor?
 
Because this equation is under the cauchy-euler section of my book, so I am trying to figure out how it is done even though its not linear. Does anybody know if its possible to solve this as a cauchy-euler equation?
 
In that case, I believe you can multiply throughout by x and solve it so.
 
Actually, the diff. eq. is linear. Why do you think it's not?
 
jofree87 said:
xy'' + y' = 0

Is it ok to multiply this whole equation by x to make it a cauchy-euler equation?

Definitely yes, although as others have pointed out, that isn't the only way. But it is easy and quick.
 

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