Characteristic Lines for 2D Equations with a Boundary Condition

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Homework Help Overview

The discussion revolves around finding characteristic lines for a specific 2D equation involving a boundary condition. The subject area includes differential equations and characteristics in mathematical physics.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to derive the characteristic lines using a specific method involving parameters a, b, and c. Some participants question the validity of the approach, particularly the inclusion of 't' instead of 'y' in the context of the problem. Others note the absence of a 'y' in the original equation and seek clarification on the boundary condition provided.

Discussion Status

The discussion is ongoing, with participants providing feedback on the original poster's attempt. There is a mix of interpretations regarding the equation and boundary condition, and some guidance has been offered regarding the expectations of the problem setup.

Contextual Notes

The boundary condition stated is u(x,0) = x^(2), which may influence the interpretation of the characteristic lines. There are concerns about the appropriateness of the variables used in the original poster's response.

andrey21
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Find the characteristic lines for the equation:

2 du/dx + 8x du/dt = 16x




Here's my attempt

a = 2 b = 8x c = 16x

Using dt/dx = b/a = 8x/2 = 4x

t = 2x2 + C

C = t1 -2x12

Hence the characteristic is:

t = 2x2 + t1 - 2x12
 
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Please any reply would be great, am I correct with my answer??
 
1. You can't expect people to anwer within two hours. People don't just sit around waiting for a new post!

2. You can get yourself an infraction and even banned for "bumping" threads just to get them moved to the top of the list again.

3. I don't even understand your answer. The characteristic is a relation between x and y. There is no "y" in your answer but there is a "t" which shouldn't be there.
 
All of the examples I have been given they do not contain a "y", I should have stated the boundary condition is u(x,0) = x^(2).
 

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