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dx? 1. f (x) = x2 and thus, as we will learn, f ′(x) = 2x. Find a differential equation for f . For this example, it should be of the form f ′(x) = f (x) ∗ g(x) where your task is to find g(x). g will not be defined at x = 0, but don’t worry about that right now.

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LammettHash

This boils down to simple algebraic manipulation.

[tex]f'(x)=2x\implies\dfrac{f'(x)}2=x\implies\dfrac{xf'(x)}2=x^2=f(x)[/tex]

So one possible ODE (the simplest, in fact) is

[tex]f'(x)=\dfrac2x f(x)[/tex]

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