Question

If f(x) = x^2, and f'(x) = 2x. Find a differential equation for f. For this example, it should be in the form of f'(x) = f(x) * g(x). Find g(x)?

Answer 1

i guess \(g(x)=\frac{2}{x}\) since
\[x^2\times \frac{2}{x}=2x\]