Timeline for differential equation of conics
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| Sep 11, 2015 at 13:32 | comment | added | Robert Bryant | Think of it the other way: The second derivative of $(x^2+c)^{1/2}$ so must be an even function of $x$ and so must be an even polynomial $p(x)$ times $(x^2+c)^{-3/2}$. Since $(x^2+c)^{1/2}$ is like $|x|$ when $|x|$ is large, its second derivative must go to zero for $|x|$ big, the degree of $p$ must be less than $2$, so it must be a constant (nonzero when $c$ is not zero). | |
| Sep 10, 2015 at 18:34 | comment | added | Fedor Petrov | Well, in such direct approach what does astonish me is why second antiderivative of $(x^2+c)^{-3/2}$ equals $(x^2+c)^{1/2}$. It may sound stupid, and it is, but why? Before integrating I expect something more involved. | |
| Sep 9, 2015 at 9:54 | history | answered | Robert Bryant | CC BY-SA 3.0 |