All Questions
4
questions
0
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1
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71
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Intuitively, why does growth proportional to the population size not diverge but growth proportional to pairs diverges to infinity in finite time?
It's interesting that growth which is proportional to the current population doesn't diverge to infinity, while growth that is proportional to higher powers of the current population.
That is, the ...
- 1,489
3
votes
7
answers
615
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Intuitive explanation of $y' = y \implies y = Ce^x$
I understand why $f : \mathbb{R} \to \mathbb{R}$ with $f'(x) = f(x)$ and $f(0) = 1$ must be $f (x) = e^x$, but I don't really feel it is super intuitive. Intuitively, why would you expect such a ...
- 1,872
10
votes
3
answers
263
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Physical intuition for the solution to $y' = y$.
Assume that $e^x$ has not been defined, so please do not refer to $e$ in an answer.
Given the D.E $y' =ry$, we substitute a power series and arrive at the solution:
$$y = \sum_{k =0}^\infty \frac{(rx)^...
- 714
3
votes
3
answers
303
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Understanding solution to $y' = y$ and exponential distribution
My Understanding:
I would derive the exponential random variable as follows:
I consider an experiment which consists of a continuum of trials on an interval $[0,t)$. The result of the experiment ...
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