You must take the second derivative of y. Can you do that or you want help?
Here is the thing that I still see here:
If , where A, B and k are constants, show that
OK: Thanks to y not being a function of x, the derivative zeros that. So then you still have:
to deal with. It really does not make sense as a question unless there is some part missing that makes the solution something along the lines of what ManosG posted. Without a derivative to cancel out that part, it is simply not true that it = 0.
What is the source of the question?
I ask because if something can be either true or false it generally starts with "If possible...." This one just says "show that" which usually means it is true and you are doing a proof. However, the way it has been stated seems to not allow for it to be true, so not a proof. Therefore, there must be a problem somewhere.
The only two places I see a possible problem are either in the source or how it has been copied. If it is the source, not much can be done other than to complain or assume they meant to write it differently. If it is how it is copied, all it would take would be something like a notation for the set of problems this is on, a missing f(t) type statement, or just those words, "If possible..."
Yes Plato, you may have a point, but the exercise does not say "find the t for which d^2y/dx^2+K^2y=0 ", it says "show that d^2y/dx^2+K^2y=0 ", so it makes no sense the "K^2y=0". I believe, he has written false the equation and the right answer is to take the second derivative