desolve y'=(x+y)^2

[salvomic]

(05-02-2015 04:45 PM)Tugdual Wrote:  I have been able to achieve some results with Maxima and contrib_ode.
But so far the ClassPad 400 is way above the rest and could successfully solve all equations.

well.
ClassPad 400 can solve also Riccati equation?
\[ y' + \frac{2x+1}{x}y - \frac{1}{x}y^{2} = x+2 \]

thank you.

[Tugdual]

(05-02-2015 04:59 PM)salvomic Wrote:  

(05-02-2015 04:45 PM)Tugdual Wrote:  I have been able to achieve some results with Maxima and contrib_ode.
But so far the ClassPad 400 is way above the rest and could successfully solve all equations.

well.
ClassPad 400 can solve also Riccati equation?
\[ y' + \frac{2x+1}{x}y - \frac{1}{x}y^{2} = x+2 \]

thank you.

Not 100% the same form as the solution you gave but quite close and definitely correct.
Off topic note: too bad this little evil doesn't have MES or unit of measuremernt like the 50g.

[salvomic]

(05-02-2015 05:21 PM)Tugdual Wrote:  Not 100% the same form as the solution you gave but quite close and definitely correct.

quite well

[parisse]

(05-02-2015 12:49 PM)salvomic Wrote:  EDIT:
please, Parisse, help:
I see two links:
http://www-fourier.ujf-grenoble.fr/~pari...ble.dmg.gz
http://www-fourier.ujf-grenoble.fr/~pari...sx6.dmg.gz

but that both here download the same (unstable) version...

They are not the same

Code:


-rw-r--r-- 1 parisse ensch 63880109 mars  27 12:38 xcas_osx6.dmg.gz
-rw-r--r-- 1 parisse ensch 63972197 avril 28 13:32 xcas_osx6_unstable.dmg.gz

Beware that the dmg name once opened by the disk mounter is the same.

[salvomic]

(05-02-2015 06:15 PM)parisse Wrote:  They are not the same

Code:


-rw-r--r-- 1 parisse ensch 63880109 mars  27 12:38 xcas_osx6.dmg.gz
-rw-r--r-- 1 parisse ensch 63972197 avril 28 13:32 xcas_osx6_unstable.dmg.gz

Beware that the dmg name once opened by the disk mounter is the same.

right!

In about I get "xcas 1.1.4-19 (c) 2000-14, Bernard Parisse...", I presume it's the latest, however...

If so, it's ok.

[salvomic]

(05-02-2015 05:30 AM)parisse Wrote:  Xcas can solve this equation. It is a Ricatti equation, you can solve it by giving a particular solution, otherwise the system rewrites it as a 2nd order equation.

please, can you explain a practical example to try?
thank you

[parisse]

Without solution desolve(y'=(x+y)^2)
With particular solution (here a complex one) desolve(y'=(x+y)^2,x,y=-x+i)

[salvomic]

(05-03-2015 06:08 AM)parisse Wrote:  Without solution desolve(y'=(x+y)^2)
With particular solution (here a complex one) desolve(y'=(x+y)^2,x,y=-x+i)

ok, but I must set something?
I mean, also so, in XCas I get [] (see image) and no solution, always...

[parisse]

Check that version() returns 1.2.0. If not, you must install the unstable version.

[salvomic]

(05-04-2015 07:15 AM)parisse Wrote:  Check that version() returns 1.2.0. If not, you must install the unstable version.

as I noted above, I had xcas 1.1.4-19 (c) 2000-14
now I've installed 1.2 unstable and with the general equation I get
\[ \frac{\mathrm{c\_1} \sin\left(x\right)-\mathrm{c\_2} \cos\left(x\right)-\mathrm{c\_1}\cdot x \cos\left(x\right)-\mathrm{c\_2}\cdot x \sin\left(x\right)}{\mathrm{c\_1} \cos\left(x\right)+\mathrm{c\_2} \sin\left(x\right)} \]
then, with trigtan() ->

\[ \frac{-\mathrm{c\_1}\cdot x+\mathrm{c\_1} \tan\left(x\right)-\mathrm{c\_2}\cdot x \tan\left(x\right)-\mathrm{c\_2}}{\mathrm{c\_1}+\mathrm{c\_2} \tan\left(x\right)} \]

(trying your advise, \( \mathrm{desolve}\left(y'=(\left(x+y\right)^{2}),x,y=(-x+i)\right) \) the result is \( [-x+i,\frac{4}{4\cdot \mathrm{c\_1} e^{-2*i\cdot x}+2*i}-x+i] \))

***
I tried also the Windows version, but the stable is still 1.1.4.19 also...

[salvomic]

also with resolve(y'=-y^2,t,y) in the Prime I get [], while in the last XCas the correct answer is 1/(t+c_0)
I hope they release soon a new firmware almost with the new XCas improvements :-)

Salvo