Solve the first order hyperbolic equation

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Homework Help Overview

The discussion revolves around solving a first order hyperbolic equation given by 3 du/dx + 2x du/dt = 2u, with an initial condition of u(x,0) = 2x + 4. Participants explore various methods for approaching the problem, particularly focusing on the method of characteristics.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the method of characteristics, with one participant presenting their characteristic equations and initial conditions. Others express uncertainty about the correctness of their methods and seek clarification on specific steps, such as integrating and solving for constants.

Discussion Status

The discussion is active, with participants providing guidance and feedback on each other's approaches. There is a collaborative effort to clarify methods and resolve confusion regarding the integration and application of initial conditions. Multiple interpretations of the problem-solving process are being explored.

Contextual Notes

Participants are navigating through the complexities of the method of characteristics and the implications of initial conditions. There is an acknowledgment of potential confusion regarding the integration steps and the evaluation of constants.

  • #31
Plug it in and see what sign causes you trouble (I think it'll be the - sign that will be the troublesome one). Look for large values of x to find the right sign. Then you're done, you've got the right solution!
 
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  • #32
Which equation shall I plug the r value into?

Is it:

log u = x2/3 + log (2r+4) - r2/3
 
  • #33
Yes.
 

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