A problem in differential equation

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Discussion Overview

The discussion revolves around a problem in differential equations, specifically focusing on the application of the chain rule and the computation of derivatives. Participants are exploring the steps necessary to solve the problem presented in a linked exam document.

Discussion Character

  • Homework-related

Main Points Raised

  • One participant shares a link to an exam problem, indicating it is the basis for the discussion.
  • Another participant presents a formulation of the chain rule, suggesting a method for differentiating with respect to x.
  • A subsequent post expresses uncertainty about the next steps to take in solving the problem.
  • Another participant provides a second derivative expression, relating it to the function f and its partial derivatives, indicating that the values of f and its first order partial derivatives are known from the problem statement.

Areas of Agreement / Disagreement

The discussion does not appear to reach a consensus, as participants are at different stages of addressing the problem and expressing uncertainty about the next steps.

Contextual Notes

There may be limitations regarding the clarity of the problem statement and the assumptions underlying the application of the chain rule, as well as the specific definitions of the variables involved.

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by the chain rule
[tex]\frac{d}{dx}=\frac{\partial}{\partial x}+\frac{dy}{dx}\frac{\partial}{\partial y}[/tex]
 
What to do next...
 
[tex]\frac{d^2 y}{dx^2}=\frac{df}{dx}=\frac{\partial f}{\partial x}+f \frac{\partial f}{\partial y}[/tex]

the values of f and its first order partials are known from the problem statement
 

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