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if f'(x) =a f(x) for all x, then f(x) =A exp (ax) for some constant A;

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"Constancy Theorem"? – David Mitra Feb 27 '14 at 15:17
Perhaps, see this. – David Mitra Feb 27 '14 at 15:22
Thanks you for the link! – Sean Willington Feb 27 '14 at 16:03
up vote 1 down vote accepted

Hint: Let $G(x)=\frac{f(x)}{e^{ax}}$. Differentiate. The derivative simplifies a lot!

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