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Diff equations: about _t38
02-04-2015, 06:37 PM (This post was last modified: 02-04-2015 08:34 PM by salvomic.)
Post: #1
Diff equations: about _t38
hi,
having to solve a differential equation (t^2*y'=y^2+ty+t^2) in t (time) and y, with desolve I get a message from Terminal, "Homogeneous", than something like [-i*t i*t [G_0*e^ATAN(_t38) G_0*_t38*e^ATAN(_t38)]]

What's, exactly, "_t38"?
Is it possible to simplify in any way?

I should have y(t)=t*TAN(log(|t| + c), as substituting z=y/t and so on...

Generally speaking, I that G_0 is an heritage of the Queen HP50, but perhaps it would be also nice can change it into c0 (or c_0) without use always "subst()"...

Thank you in advance for info

Salvo

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02-04-2015, 07:31 PM
Post: #2
RE: Diff equations: about _t38
The third solution is a parametric solution, expressed in terms of a mute variable, here named _t38.
Some mute variable names comes from the 38 variable names, not from the 48/49/50 (otherwise you would get the same constant names as in Xcas).
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02-04-2015, 08:38 PM
Post: #3
RE: Diff equations: about _t38
(02-04-2015 07:31 PM)parisse Wrote:  The third solution is a parametric solution, expressed in terms of a mute variable, here named _t38...

ok, understood, thanks. Odd name, however

And the other solutions?
I thought to have some real solution, not complex...
A general solution should be y(t)=t*TAN(log(|t| + c), however...

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02-05-2015, 07:09 AM (This post was last modified: 02-05-2015 08:49 AM by parisse.)
Post: #4
RE: Diff equations: about _t38
You can indeed solve for t in x=the first coordinate of the parametric solution and get y as a function of x, but this can not be done in general for an homogeneous differential equation. The first two solutions are particular solutions, they are complex here therefore you can omit them if you solve in the real domain, but this is not true in general.

[Edit]
I'm going to add code to try solving for t in x and remove non real singular solutions (in real mode).
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02-05-2015, 03:12 PM
Post: #5
RE: Diff equations: about _t38
(02-05-2015 07:09 AM)parisse Wrote:  I'm going to add code to try solving for t in x and remove non real singular solutions (in real mode).

thank a lot!
Please, let me know, then... Smile

Salvo

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02-05-2015, 04:24 PM
Post: #6
RE: Diff equations: about _t38
Should be in the unstable versions of Xcas.
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02-05-2015, 04:35 PM
Post: #7
RE: Diff equations: about _t38
(02-05-2015 04:24 PM)parisse Wrote:  Should be in the unstable versions of Xcas.

great!
;-)

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05-13-2015, 08:29 PM
Post: #8
RE: Diff equations: about _t38
Now, with firmware 7820 I get
t*TAN(LN(t/G_0))
ok.

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