Differential Equation: 1st-Order in Time, 2nd-Order in Space

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Discussion Overview

The discussion revolves around the classification of a differential equation that features first-order derivatives in time and second-order derivatives in space. Participants explore the implications of these classifications in terms of order and how they relate to solving partial differential equations (PDEs).

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant asks about the order of a differential equation with first-order time and second-order space derivatives.
  • Another participant asserts that the order is determined by the highest derivative, indicating that it is a second-order PDE.
  • A third participant suggests that it is also valid to specify the order in terms of individual variables, stating it is second order in space and first order in time.
  • A fourth participant notes that while the specific classification is valid, the highest order is what matters for solving the PDE.
  • This participant then poses a question regarding the classification of a specific equation, asking whether it should be considered first order in time and space or second-order in both.

Areas of Agreement / Disagreement

Participants generally agree on the principle that the order of a differential equation is determined by the highest derivative. However, there is some contention regarding the importance of specifying the order with respect to individual variables and how to classify certain equations.

Contextual Notes

There may be limitations in the discussion regarding the definitions of order and classification, as well as the implications of these classifications for solving PDEs. The specific equation mentioned remains unresolved in terms of its classification.

saravanan13
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what is the order of differential equation which contains first order in time and second order in space derivative?
 
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it will be the order of the highest derivative (doesn't matter in respect to what variable).
In your case, it's a second order pde
 
Although it would also be perfectly acceptable to say "The differential equation is of second order in x and first order in t".
 
It is a more specific classification

But in respect to how you solve the PDE, it's only important what's the highest order.

In this matter, how would you classify [tex]u_{xt}+blabla=0[/tex], first order in time and space, or second-order in both?
 

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