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HallsofIvy

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In particular, the usual "existence and uniqueness" theorem is this: If (t

Second or higher order problems can be handled in the same way by defining x

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Actually I saw in a paper the author deals with three variables: m(x), n(x) and V(m). Now he had three differential equations involving m'(x), m"(x), n(x)^2 and dV/dm. This was not an initial/boundary value problem. Just the functional forms for the dependent variables were needed. Now he had shown that for different choices of m(x), he could get different sets for n(x) and V(m). While reading this the question I had posed came to my mind--i.e., can we say how many functional forms of the solutions are possible?

Your answer was from a different point of view. But there was something for me to learn. Thanks for answering. If you have any comment on the detailed version of the problem I have given here, please write that also.

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