Talk:Ordinary Differential Equations/Homogenous 1

incorrect general snl?
Many times under Class 3a, the claim is made that the general sln to


 * $$\frac{d^2y}{dx^2}+\omega^2 y=0$$

is


 * $$y=A\sin \omega x+B\sin \omega x \,$$

I believe this to be wrong, as you can simplify this to


 * $$y=(A+B)\sin \omega x \,$$

leaving yourself with an incomplete sln. I made the edit, then noticed 3 places where this (mistake?) occurs and decided to revert my edit and ask here. I do believe (via mo knowledge of the subject and following the math leading up to the sln) that the correct sln is


 * $$y=A\sin \omega x+B\cos \omega x \,$$

Am I missing something, or was this a mistake?

Slithytove2 22:18, 24 September 2006 (UTC)