MHB Showing Superposition: u(x, t) Equation

[jmorgan]

Hi, I can't quite understand how to do this question please could someone help :)

Show, by the principle of superposition, that

u(x, t) =
∞
∑ A_n sin(npix)e^2n2pi2t
n=1

where A1, A2,..., are arbitrary constants.

Thanks

 

[Greg]

Hello jmorgan and welcome to MHB! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?

 

[I like Serena]

Hi, I can't quite understand how to do this question please could someone help :)

Show, by the principle of superposition, that

u(x, t) =
∞
∑ A_n sin(npix)e^2n2pi2t
n=1

where A1, A2,..., are arbitrary constants.

Thanks

Hi jmorgan! ;)

It appears that your problem statement is incomplete.
It seems to me there should be a differential equation and a set of solutions that is already known.
The principle of superposition means that for a linear homogeneous ordinary differential equation any linear combination of known solutions is also a solution.
Can you clarify? (Wondering)