non-homogenous solution to PDE with difficult Boundary Cond.

Jan 2013
6
0
Dear all,

I am new to this forum but I am preparing my graduation exam. I can not solve this question and I have been trying for the last 2 days AND NIGHTS. A friend of mine recommended this forum and I was hoping perhaps you guys could help me out, it involves the following problem;

d^2a/dx^2 = f(x)
a(0) = 0
da/dx + ha(L) = 0, at X=L

I have tried integrating directly but I can not get a nice answer. I also need to solve using the variation of parameters and write in a green's function. However, I keep getting terms which I can not possibly put into a symmetric green's function. Can someone please please please help me out here?

Thanks a lot

Greetings from Bulgaria
 
Aug 2011
334
8
Re: non-homogenous solution to PDE with difficult Boundary C

Hello !

The wording of the question is ambiguous :
In the equation d^2a/dx^2 = f(x) there is only one variable (x). So, it is not a PDE, but an ODE. Then, why do you talk of Green's function in case of an ODE ? So, there is something which is not coherent in the wording.
Now, supposing that the ODE and conditions are without typo, nevertheless it is impossible to give an explicit solution as far as the function f(x) is not explicitly given in the ODE. All that can be donne is to give a non-explicit solution involving double integral of f(x)
 

Attachments

Jan 2013
6
0
Re: non-homogenous solution to PDE with difficult Boundary C

Thank you for your help. Really, I appreciate it a lot, i was working on this question for many hours. I do need to get a green's function using variation of parm, it is indeed written as a ODE; d^a/dx^2 = f(x) with the given BC's, however now I need to find a green's function, in the form G(x, xo). I've tried to get it and i keep getting something weird, but it's not symmetric. :shock:
 
Jan 2013
6
0
Re: non-homogenous solution to PDE with difficult Boundary C

I only have this of the question (the solution only but not the steps taken to get the solution of this question) but I need to find this using varia of parm. but I just cant get it. I keep getting an extra integral which I can not possibly write into Greens.
 

Attachments