What's the difference between these two D.E?

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Homework Help Overview

The discussion revolves around two differential equations: 1) x(x-1)y``+(3x-1)y`+y=0 and 2) (x^2 -x)y``-xy`+y=0. Participants are exploring the differences in methods used to solve these equations.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the methods used for solving each differential equation and discussing the appropriateness of terminology related to the Frobenius method.

Discussion Status

The conversation is focused on understanding the different approaches to solving the two equations, with some participants providing insights into the methods used. There is an ongoing clarification regarding the terminology associated with the Frobenius method.

Contextual Notes

There is a noted concern about the misuse of the term "Frobenius" in relation to the equations, as participants clarify that this term specifically refers to power series solutions.

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1. x(x-1)y``+(3x-1)y`+y=0
2. (x^2 -x)y``-xy`+y=0
those are 2 examples of the frobenius method, but i don't understand why those 2 use completely different methods to solve...
 
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What methods were used to solve each of them?
 
the first used the method of variation of parameters, and the second one
supposed that y2=cy1 and differentiated that and subsituted y2``, y` and y into the original equation...
 
Firstly, can you stop calling DEs frobenius: they are not. Frobenius refers to the use of a power series solution for DEs, there are different ways to work out what that power series is.
 

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