Re: differential equation question

In article <1138611173.575600.184650@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
asdf <qjohnny2000@xxxxxxxxx> wrote:
>how do you show that the ONLY solutions to f(x) + f''(x) = 0,
>are of form Acos(x) + Bcos(x), where A and B are constants ?
>Just give a hint .. this is homework problem... what track should I go
>down.
>I was thinking of power series type of thing.

No, don't use power series unless you know a theorem that says all
solutions must be analytic. But if you know that theorem you
must certainly know an Existence and Uniqueness Theorem for
differential equations. If you really need to do it from scratch
without such a theorem, you might start by showing that
f^2 + (f')^2 is constant.

Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.

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