Special Second Order Ordinary Diff. Equation

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Discussion Overview

The discussion revolves around solving a special second-order ordinary differential equation (ODE) as part of constructing a Green's function. Participants are exploring the nature of the equation, particularly focusing on the homogeneous solution and the role of the function P and the constant k.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant expresses uncertainty about how to solve a specific second-order ODE encountered in their studies.
  • Another participant notes that the solution may depend on the nature of P, suggesting that if k is not constant, the equation could be a fourth-order, non-homogeneous ODE.
  • A participant clarifies that P is a function of x and k is a constant, emphasizing their focus on solving the homogeneous equation.
  • There is a suggestion that the general method for solving these types of ODEs involves using infinite series, although the specifics of the function P are questioned.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the specifics of the function P or the best approach to solve the homogeneous equation, indicating that multiple views and uncertainties remain in the discussion.

Contextual Notes

The discussion does not clarify the exact form of the function P, which may affect the method of solution. There are also unresolved aspects regarding the assumptions made about the equation's order and homogeneity.

Andreol263
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Hello guys, I'm studying from Green's Function With Applications by Duff, and he finds the general solution(homogeneous sol.) to this differential equation:
BBg5D4l.png
, but i I've never seen a equation like this before, how can i manage to solve this equation??
 
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Andreol263 said:
Hello guys, I'm studying from Green's Function With Applications by Duff, and he finds the general solution(homogeneous sol.) to this differential equation:
BBg5D4l.png
, but i I've never seen a equation like this before, how can i manage to solve this equation??
It depends on what P is. I assume that k is a constant. Otherwise, you have a fourth-order, non-homogeneous ODE.
 
P is only function of x, and k is indeed a constant, but I'm trying to solve the homogeneous eqn, that it's part of constructing the green function of this equation, how i solve the homogeneous one??
 
Andreol263 said:
P is only function of x, and k is indeed a constant, but I'm trying to solve the homogeneous eqn, that it's part of constructing the green function of this equation, how i solve the homogeneous one??
If P is a function of x, what sort of function is it? The general method of solution to these types of ODEs is by infinite series.

http://tutorial.math.lamar.edu/Classes/DE/SeriesIntro.aspx
 

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