Second order differential equation form

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Discussion Overview

The discussion revolves around the interpretation of a second order differential equation in the form d²y/dx² = f(x, y, dy/dx). Participants are exploring how to understand the right-hand side of the equation and its relationship to the left-hand side.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • Some participants propose that the right-hand side (RHS) is a function of x, y, and dy/dx, providing an example of x²y - 3dy/dx.
  • Others express a need for clarification on how the RHS relates to the left-hand side (LHS) and question the concept of "expanding" the RHS to the LHS.
  • A later reply challenges the idea of expansion, suggesting that the relationship between the RHS and LHS depends on the specific function and does not imply a direct expansion.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the interpretation of the RHS in relation to the LHS, indicating that multiple views remain on how to approach the relationship between the two sides of the equation.

Contextual Notes

Limitations include the dependence on the specific form of the function f(x, y, dy/dx) and the ambiguity surrounding the term "expand." The discussion does not resolve these aspects.

negation
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A second order differential equation form d2y/dx2 = f(x,y,dx/dy)

How do I read the language on the right hand side?
 
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negation said:
A second order differential equation form d2y/dx2 = f(x,y,dx/dy)

How do I read the language on the right hand side?
The righthand side is some function of x, y, and dy/dx. For example, it could be x2y - 3dy/dx.
 
Mark44 said:
The righthand side is some function of x, y, and dy/dx. For example, it could be x2y - 3dy/dx.

I know that. I should have been more explicit. How does the RHS (expand?) to the LHS?
 
What Mark44 said is all you can say. How you "expand" it or if you can depends upon the exact function. And it certainly does not expand "to" the LHS, any more than the "f(x)" in "y= f(x)" expands to "y".
 

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