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!
Ah, so you're saying I found a solution to the BVP? Then how would I go about showing this. I have no idea. If I make choose the general solution to be of the form Ax + B, then I'll get A = 0 for both boundary cases. Meaning the answer to the BVP is y(x) = B...
is the first derivative of a solution satisfying the condition, the other condition then requires that:
So the boundary value problem cannot have a solution if
If this integral is zero then the solution is:
We note that is not a condition independed of , which is why in solution to the boundary value problem we still have an arbitary constant.