How do I set up the following Differential Equation?

Question

so in the following word problem, it seems that I am supposed to solve a differential equation in order to find the function f. However, with the way it is worded, I'm having a tough time actually figuring out what the differential equation is. Can anyone help explain what the word problem is actually telling me? Thank you!

Answer 1

The problem says $f(x)=2f'(x)$,

so $f'(x)=\frac12 f(x).$

Can you solve that differential equation?

Answer 2

$$2\frac{df}{dx}=f\implies \int \frac{2d f}{f}=\int dx+C \implies \ln f^2=x+C \implies f^2=De^{x} \implies D=4$$ Hence $$f(x)=2e^{x/2}.$$