differential equations

05022019, 08:36 AM
Post: #1




differential equations
the calculator I throw the solution of a differential equation (this: y '''+ y''= 8 * x ^ 2) that I think is wrong, because it is too long and because it has things that should not take the solution (this : 16 * e ^ ( x) + G_0G_2)
this is the complete answer that the hpp throws at me: G_1 * x + G_2 * e ^ ( x) + (2/3) * x ^ 4 (8/3) * x ^ 3 + G_2 * x + 8 * x ^ 216 * e ^ ( x ) + G_0G_216 * x + 16. and if there is a way to fix it? If there is not, please notify hp about this error PS: can I upload screenshots that I made to my calculator that I have stored on my computer here about this problem? If so, how? 

05022019, 10:58 AM
Post: #2




RE: differential equations
It's a 3rd order linear diff eq with cst coefficients, therefore you must have 3 arbitrary constants of integration.


05062019, 05:59 AM
Post: #3




RE: differential equations
So is the result okay?


05062019, 06:31 AM
(This post was last modified: 05062019 07:58 AM by ijabbott.)
Post: #4




RE: differential equations
I guess G_0G_2+16 could be replaced with just G_0.
EDIT: and G_1*x+G_2*x could be replaced with just G_1*x. — Ian Abbott 

05062019, 12:09 PM
Post: #5




RE: differential equations  
05062019, 09:35 PM
(This post was last modified: 05062019 10:19 PM by Anders.)
Post: #6




RE: differential equations
This is another example of where the CAS system does not return the result in a canonical form. Unfortunately, it also happens in a few places, e.g. various transformations like Laplace, Z etc. While CAS produces mathematically correct results, it is sometimes far away from what the user expects (canonical form) and it takes time (some times a lot of time) to figure out how to convert the result into a familiar form that the user can interpret and understand it's physical meaning (e.g. in physics, EE, control theory etc).
Since CAS is not using table look up as a method to produce results but is using generalized algorithms (which I think is actually a strength because it can therefore cover more complex situation generally). However, it would be great to have a sort of normalization algorithm as a last step that the user could invoke (kind of like the "simplify" button) to normalize a result into canonical form and/or with an option to auto normalize (through a setting). I've been toying with the idea to write a program that does this. I was thinking write a parser that parse the input and call CAS termwise and then have the program put together the result in canonical form, but it became too complex because you have to normalize the input first anyway. So some work. 

05062019, 10:08 PM
(This post was last modified: 05062019 10:09 PM by Anders.)
Post: #7




RE: differential equations
(05062019 12:09 PM)Aries Wrote:Thank you for showing that Nspire can produce canonical form answers! It looks nice.(05062019 05:59 AM)eduardo_MO0@hotmail.com Wrote: So is the result okay? However, Nspire CAS is not a serious contender to HP Prime's CAS. From what I can tell, (reading the Nspire CAS reference manual and more) Nspire CAS in it's native form, does not cover any transforms (e.g. Fourier and Lapace etc and more) making it nearly useless for the serious engineering student. It will barley get them through the first year  maybe differential equations 101 without Fourier and Lapace etc. (you need to do those transformations yourself). So no, Nspire is not the answer  not even close. HP Prime has a much more powerful underlying CAS engine. What's left is to polish the presentation of the results. Best 

05072019, 01:39 AM
Post: #8




RE: differential equations
thank you for confirming that the result of my calculator is correct


05072019, 06:23 AM
Post: #9




RE: differential equations
Constant of integrations are choosen so that the solution at x=0 is G_0, the derivative of the solution at x=0 is G_1 and so on. That way, finding the solution with initial conditions at x=0 is straightforward.


05102019, 02:01 PM
Post: #10




RE: differential equations
(05062019 10:08 PM)Anders Wrote:(05062019 12:09 PM)Aries Wrote: I think the result is correct, by comparison here is the Nspire result:Thank you for showing that Nspire can produce canonical form answers! It looks nice. Hi Anders, thirdparty libraries are fully supported by TI, some of them (linalg and numtheory) are included in the O.S. so I don't see any problem with Ltransforms, Fourier series/transforms, Ztransforms, convolution, control systems theory and so forth. Power of the calculator also relies on the support of the international community and the Nspire community base is highly active. Best, Aries 

05112019, 05:26 AM
(This post was last modified: 05112019 06:40 AM by Anders.)
Post: #11




RE: differential equations
(05102019 02:01 PM)Aries Wrote:(05062019 10:08 PM)Anders Wrote: Thank you for showing that Nspire can produce canonical form answers! It looks nice. That is just the point: 3rd party libraries extends programable calculators so they can do stuff they could not do originally. As I am sure you are already know, both platforms have extensive collections of 3rd party libraries. HP prime have a few here for instance: https://www.hpmuseum.org/forum/forum15.html and more references to stuff here: https://www.hpmuseum.org/forum/thread818.html. BTW you can also install XCAS on TI Nspire so you can actually get the CAS functionality on par withy HP Prime if you want. But the point is that more 3rd party stuff you do, the more they are no longer the calculators you are trying to compare (because comparing is what you were doing). It's obviously no apples to apples comparison any more. For instance, I can also program (and indeed I did) my old HP42S, HP28S, HP48, HP50 and so on to do all sorts of stuff. Here is the thing: the point with many threads on this forum is for users to ask questions, propose stuff and highlight issues with the current HP Prime version in CAS mode, numerical mode (Home) and elsewhere so that HP and the community around can improve the HP Prime to do as much as possible NATIVELY, WITHOUT resorting to 3rd party stuff. And as I wrote before, NATIVELY, TI Nspire cannot do remotely the same advanced stuff that HP Prime can  it's just a fact. Just take some time to read: https://wwwfourier.ujfgrenoble.fr/~par...me_cas.pdf and you quickly see the native power of HP Prime CAS. No HP Prime it's not perfect (yet) but we are trying to help to improve it to become better and better. One thing is sure though, out of the box, HP Prime is the most advanced CAS calculator in existence (not counting phone apps like Wolfram alpha with the whole cloud compute behind). Native TI Nspire seams to be years behind. I mean HP prime was released in 2013 and so far, TI Nspire CAS response has been (the way I read it from an user's perspective) to open up the platform to 3rd party stuff. BTW HP could decide to take the same approach if they wanted to, but doing so would create problems with some testing authorities I believe. Best regards 

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