TITLE: Conceptual question on differentiation in calculus?
QUESTION [5 upvotes]: In Calc class, my teacher told us that the only solution to $y' = y$ is $y = ce^x$, with $c$ being a real number. I am having difficulty understanding the only part. Is there a proof of this? Or am I missing something obvious?

REPLY [3 votes]: Expanding on Matthew's comment
Let $g(x)=f(x)/e^x$. Then, $g'(x)=\frac{f'(x)e^x-f(x)e^x}{e^{2x}}=0$ Therefore, $g(x)$ is a constant say $C$.
Then,
$f(x)=Ce^x$