PDE Question

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?

The Attempt at a Solution

∂^2 f/∂x^2 = exp(x-ivt)

and

∂f/∂t = -iv exp(x-ivt)

Possible if v = -i

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Ray Vickson
Homework Helper
Dearly Missed

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?

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 $\partial^2 f/\partial t^2, \text{ not just } \partial f/\partial t.$ Anyway: what is "c"? The PDE does not have "c" in it, nor does your f.

RGV

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.

You need to compute $\partial^2 f/\partial t^2, \text{ not just } \partial f/\partial t.$

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)