Gotta BVP here that I'd like to run by someone to see if my thinking is correct.
Show that the following boundary value problem:
does not in general have a solution.
I used the LDE solution to be .
So, solving for both boundary conditions:
This, to me, shows that there is no solution of this form to the BVP. Is this sufficient to answer the question?
The next part asks to find a condition of for there to be a solution. If choose the boundary conditions of , and making the right boundary condition to be , I'll get a solution of the form .
Am I close? Or have I got the wrong idea here.
Thanks for your time!