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# f'(x) = x^2 f(x) watch

1. How do I prove that

is equal to

2. I'm not sure what you actually mean by what you've just written.

The two are not logically equivalent: the 2nd equation implies a specific value for f(1), while the 1st equation only describes the derivative and so f is not unique (adding a constant to f will not stop it satisfying the 1st equation).

3. This is what i mean, sorry
4. Replace by in the first series and rearrange stuff. Things will cancel.
5. (Original post by Dagnabbit)

This is what i mean, sorry

If you wanted to you could it like this:

Rearrange the equation a bit to get

Notice that by the series definition of an exponential

This implies that

Differentiate both sides with respect to x (need the chain rule for the LHS)

Multiply both sides by f(x)

Which is what you wanted

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Updated: March 27, 2011
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