Need explanation for simple differential equation I can't figure out this really simple linear equation: $$x'=x$$ I know that the result should be an exponential function with $t$ in the exponent, but I can't really...--prophetes.ai

Need explanation for simple differential equation I can't figure out this really simple linear equation: $$x'=x$$ I know that the result should be an exponential function with $t$ in the exponent, but I can't really say why. I tried integrating both sides but it doesn't seem to work. I know this is shameful noob question, but I would be grateful for any hints.

Hint: $$\frac{dx}{dt}=x \Leftrightarrow dt=\frac{1}{x}dx$$