Short-answer question on characteristics of p.d.e

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Homework Help Overview

The discussion revolves around a partial differential equation (p.d.e) characterized by the expression ut − 2ux = 1/u. Participants are exploring the characteristics of the equation and what expressions remain constant along these characteristics.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to identify constant expressions along the characteristics and presents specific expressions derived from their reasoning. Some participants question whether the original poster has quoted the question accurately and suggest that a more general answer may be required.

Discussion Status

The discussion is ongoing, with participants providing feedback on the original poster's attempts. There is a suggestion to consider the implicit form of the solution to include all branches of the square root function, indicating a productive direction in the exploration of the problem.

Contextual Notes

There is a mention of the second branch of the square root function being overlooked, which may affect the completeness of the original poster's answer. The need for precision in quoting the question is also highlighted.

Maximtopsecret
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Homework Statement


ut − 2ux =1/ u;
what expressions are constant along the equations's characteristics?

Homework Equations


3. The Attempt at a Solution [/B]
Am I right?
dt=dx/(-2)=du/(-1/u), -2t=x=u2;
u=sqrt(x); u=sqrt(-2t) are constant.
 
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I think that they may want a slightly more general answer. Have you quoted the question precisely as it was stated?
 
MarcusAgrippa said:
I think that they may want a slightly more general answer. Have you quoted the question precisely as it was stated?
Oh yes, the question is stated just like there...
 
Maximtopsecret said:
Oh yes, the question is stated just like there...

Then, apart from the fact that you have ignored the second branch of the square root function, your answer is correct. It may be better to quote the solution function u(x,t) in implicit form rather than to solve it explicitly for u. That way you include both branches of the square root function.
 

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