How to prove the only solution to $f(x)=f'(x)$ is $ce^x$?

Asked Apr 25 '12 at 05:49

Active Feb 02 '17 at 13:47

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Proof that $\exp(x)$ is the only function for which $f(x) = f'(x)$

I've learned from calculus that $Ce^x$ is a solution to the equation $f(x)=f'(x)$, where $C$ is a constant. However, in my Physics class the textbook takes it as the only solution to the equation without proof.

I wonder why there are no other solutions? I haven't taken the course of ODE, so I might need an elementary explanation~ Any help will be welcome~

edited Apr 13 '17 at 12:20

Community

asked Apr 25 '12 at 05:49

rhenskyyy

An answer is given by a link on this page. Go to the right side, look for the question that asks about $\dfrac{df}{dx}=3f$. – André Nicolas Apr 25 '12 at 05:52

How to prove the only solution to $f(x)=f'(x)$ is $ce^x$?

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