Concept to differential equations

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Homework Help Overview

The discussion revolves around the ordinary differential equation x^2y'' + xy' + (x^2-1)y = 0, with participants exploring the reasons for its solution's non-closed form expressibility. The subject area is differential equations, particularly focusing on the characteristics of specific types of equations like Bessel's equation.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the nature of the equation and the implications of its solutions, questioning whether series solutions are valid within the context of differential equations. There is also a mention of the context of studying singular points.

Discussion Status

The discussion is ongoing, with participants sharing their attempts to articulate the reasons behind the non-closed form solution. Some guidance is offered regarding the classification of the equation, but there is no explicit consensus on how to proceed further.

Contextual Notes

Participants note that the discussion is framed within a class on applied analysis, indicating a focus on practical applications of differential equations. There is also a reference to the professor's expectations, which may influence the direction of the conversation.

vanitymdl
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Question: Explain why you cannot solve the ordinary equation?

x^2y'' + xy' + (x^2-1)y = 0

My attempt: I don't need to solve it, but just simply state why I can't with just differential equations
So my answer is, This differential equation does have a solution, it's just not expressable in closed form.

I don't know if I should add on to this or does this get my point across
 
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vanitymdl said:
Question: Explain why you cannot solve the ordinary equation?

x^2y'' + xy' + (x^2-1)y = 0

My attempt: I don't need to solve it, but just simply state why I can't with just differential equations
So my answer is, This differential equation does have a solution, it's just not expressable in closed form.

I don't know if I should add on to this or does this get my point across

Don't series solutions qualify as "just differential equations"? Is your question given in the context of studying singular points?
 
Well this is just to refresh on my differential skills, this class is applied analysis and the professor wanted us to explain this
 

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