Timeline for Any help on one ODE
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 28, 2011 at 19:21 | vote | accept | Maksim V. Bolonkin | ||
| Dec 28, 2011 at 17:55 | history | edited | Robert Bryant | CC BY-SA 3.0 |
fixed typos
|
| Dec 28, 2011 at 16:30 | comment | added | Robert Bryant | @Maksim: Many (native English speaking) people do use 'analytical' in this antique way, but I think that it would be better to say something like 'integrable in elementary terms', even though the meaning of 'elementary terms' isn't universally agreed on either. Since your equation is of Abel type, I'd say that your best hope of integrating it in elementary terms would be to compute its invariant(s) and see whether it belongs on the list of known 'integrable' Abel equations. I'm not sure that either Maple or Matlab has programmed in all of the known 'integrable' cases, so it's worth a try. | |
| Dec 28, 2011 at 11:33 | comment | added | Maksim V. Bolonkin | Sorry for my incorrect using of "analytical" word (I use it to distiguish from numerical solution; English isn't my native language, sometimes I occasionally use calque from russian words). This is not Cauchy problem, there's no any initial conditions. Just was asked to find solution in form of $y = y(x, C)$ or $F(y,x,C) = 0$. | |
| Dec 27, 2011 at 22:50 | comment | added | Will Jagy | I did not read carefully enough. You are also teaching the OP. | |
| Dec 27, 2011 at 22:39 | comment | added | Will Jagy | Robert, thanks, I was not sure. This is one of those situations where the OP is probably not going to understand, but if you have something to teach the rest of us and patience to type it in, that's good. I would prefer that the word analytic be used only in its mathematical sense, and I used to leave comments telling the OP not to use words they did not understand. I ran out of steam on that issue, though. I'm fairly happy with an implicit description of a function, as in your example. | |
| Dec 27, 2011 at 22:26 | comment | added | Robert Bryant | @Will: I'm aware of this, but I think that this should be discouraged whenever one encounters it. 'Analytic' has a well-defined, accepted meaning, but 'closed form' is in the eye of the beholder, I think. For example, would they accept the solution of $y' = -2xy/(1+x^2+5y^4)$ in the form $y(x)^5 + (1+x^2)y(x) = y(0)^5 + y(0)$ as being in 'closed form'? I would. Would you? | |
| Dec 27, 2011 at 22:10 | comment | added | Will Jagy | Robert, various types of engineering and computer students refer to a closed form solution as analytic or analytical. Even our own Suvrit says he uses the words that way sometimes. | |
| Dec 27, 2011 at 21:36 | history | edited | Robert Bryant | CC BY-SA 3.0 |
Added information about complex solutions
|
| Dec 27, 2011 at 17:53 | history | answered | Robert Bryant | CC BY-SA 3.0 |