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PDE Question

  • Thread starter ZedCar
  • Start date
  • #1
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Homework Statement


I'm just trying to get an understanding of answering PDEs, so wanted to ask what you thought of my answer to this question.

The one-dimensional wave equation is given by the first equation shown in this link;

http://mathworld.wolfram.com/WaveEquation1-Dimensional.html

where Ψ = f(x, t)

Is f(x, t) = exp(x-ivt) a possible solution?



Homework Equations





The Attempt at a Solution



∂^2 f/∂x^2 = exp(x-ivt)

and

∂f/∂t = -iv exp(x-ivt)

Possible if v = -i
 
Last edited:

Answers and Replies

  • #2
Ray Vickson
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Homework Helper
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Homework Statement


I'm just trying to get an understanding of answering PDEs, so wanted to ask what you thought of my answer to this question.

The one-dimensional wave equation is given by the first equation shown in this link;

http://mathworld.wolfram.com/WaveEquation1-Dimensional.html

where Ψ = f(x, t)

Is f(x, t) = exp(x-ivt) a possible solution?



Homework Equations





The Attempt at a Solution



∂^2 f/∂x^2 = exp(x-ivt)

and

∂f/∂t = -ic exp(x-ivt)

Possible if v = -i
You need to compute [itex] \partial^2 f/\partial t^2, \text{ not just } \partial f/\partial t.[/itex] Anyway: what is "c"? The PDE does not have "c" in it, nor does your f.

RGV
 
  • #3
354
1
Anyway: what is "c"? The PDE does not have "c" in it, nor does your f.
Sorry, c should have been v. I've corrected it now.
 
  • #4
354
1
You need to compute [itex] \partial^2 f/\partial t^2, \text{ not just } \partial f/\partial t.[/itex]

RGV
So when I obtain the 2nd partial differentiation for 't' I obtain;

-v^2 exp(x-ivt)

So I assume this is not a possible solution since

exp(x-ivt) ≠ -exp(x-ivt)
 

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