- #1

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I was wondering. Is the exponential function, the only function where ##y'=y##.

I know we can write an infinite amount of functions just by multiplying ##e^{x}## by a constant. This is not my point.

Lets say in general, is there another function other than ##y(x)=ae^{x}## (##a## is a constant), where ##\frac{dy}{dx}=y##.

I would really appreciate it if we can work a proof.