desolve y'=(x+y)^2

[salvomic]

hi all,
there is a way to solve with Prime this kind of differential equation, like y'=(x+y)^2 ?
I get [[]]...
I should get TAN(x+G_0) - x
I'm in CAS, real mode (no complex checked)

Thank you
Salvo

[Tugdual]

(05-01-2015 02:45 PM)salvomic Wrote:  hi all,
there is a way to solve with Prime this kind of differential equation, like y'=(x+y)^2 ?
I get [[]]...
I should get TAN(x+G_0) - x
I'm in CAS, real mode (no complex checked)

Thank you
Salvo

No success here.
The 50g also fails on that one with the message "Can't find ODE type".

[salvomic]

(05-01-2015 04:11 PM)Tugdual Wrote:  No success here.
The 50g also fails on that one with the message "Can't find ODE type".

yes, in fact!
Also my 50g fails with that message...

thank you

[Arno K]

Funny, yesterday I had a similar Problem to solve, nearly the same diffeq, clearly that didn't work. So I did the Substitution u=x+y by hand, after that I entered the new equation in desolve and it worked. Itried then mathexplorer on my mobile, it didn't solve either equation. I think that this little trick can easily be implemented to the CAS.
Hth Arno

[salvomic]

(05-01-2015 04:41 PM)Arno K Wrote:  Funny, yesterday I had a similar Problem to solve, nearly the same diffeq, clearly that didn't work. So I did the Substitution u=x+y by hand, after that I entered the new equation in desolve and it worked. Itried then mathexplorer on my mobile, it didn't solve either equation. I think that this little trick can easily be implemented to the CAS.
Hth Arno

yes, I hope indeed that the substitution could be really implementable to the CAS as well.
I've tried a lot of ODE and Prime handles them well, except few types (i.e the Riccati type); this is a common form and it would be important that the Prime (and CAS) could solve it...

Another problematic form is y'= f(y/x), almost in the tries I did...

Salvo

[Tugdual]

I didn't give up but couldn't conclude.
Tried Maxima, failed.
Tried Wolfram Alpha and it found something:
$$y(x)=\frac { 1 }{ { c }_{ 1 }.{ e }^{ 2.i.x }-\frac { i }{ 2 } } -x-i$$
I checked on the 50g and this seems good but I haven't been able to relate this with a tangent...

[salvomic]

(05-01-2015 07:06 PM)Tugdual Wrote:  I didn't give up but couldn't conclude.
Tried Maxima, failed.
Tried Wolfram Alpha and it found something:
$$y(x)=\frac { 1 }{ { c }_{ 1 }.{ e }^{ 2.i.x }-\frac { i }{ 2 } } -x-i$$
I checked on the 50g and this seems good but I haven't been able to relate this with a tangent...

yes, I noted too...
However, if in Wolfram you clic on "step-by-step" you can get the trigonomtric solution (see image attached)...

[lrdheat]

(05-01-2015 02:45 PM)salvomic Wrote:  hi all,
there is a way to solve with Prime this kind of differential equation, like y'=(x+y)^2 ?
I get [[]]...
I should get TAN(x+G_0) - x
I'm in CAS, real mode (no complex checked)

Thank you
Salvo

[lrdheat]

Didn't understand how quote works...my CASIO Classpad 400 comes up with the intended answer that I quoted.

[salvomic]

(05-01-2015 07:57 PM)lrdheat Wrote:  Didn't understand how quote works...my CASIO Classpad 400 comes up with the intended answer that I quoted.

so, in Classpad 400 the result is
TAN(x+c) - x ?

thank you

[Tugdual]

(05-01-2015 08:06 PM)salvomic Wrote:  

(05-01-2015 07:57 PM)lrdheat Wrote:  Didn't understand how quote works...my CASIO Classpad 400 comes up with the intended answer that I quoted.

so, in Classpad 400 the result is
TAN(x+c) - x ?

thank you

Just checked on the emulator.
I'm impressed...

[salvomic]

(05-01-2015 08:26 PM)Tugdual Wrote:  Just checked on the emulator.
I'm impressed...
...

great!

[parisse]

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.

[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.

thank you, Parisse.
The Xcas now is more updated than the CAS on Prime...
So, we hope that in the next FW upgrade of Prime it will be ok...

the type of equation is generally y' = f(ax+by+c) and the general solution can be got substituting u (in our case u=x+y -> u'=1+y' and so on)
The classic Riccati ODE is y'+g(x)y+h(x)y^2=k(x)

I had issue with a Riccati equation like \[ y' + \frac{2x+1}{x}y - \frac{1}{x}y^{2} = x+2 \]
Prime gives [], but the solution is \[ x + \frac{1}{1+cx} \]

[parisse]

Indeed, you can also solve it by this kind of substitution. Maybe I can add another special case in desolve.
Your equation returns
(c_1*x^2+c_2*x+c_2)/(c_1*x+c_2)
with the latest Xcas. You can get your solution with c_2=1.
You are missing y=x with your general solution.

[salvomic]

(05-02-2015 10:50 AM)parisse Wrote:  Indeed, you can also solve it by this kind of substitution. Maybe I can add another special case in desolve.
Your equation returns
(c_1*x^2+c_2*x+c_2)/(c_1*x+c_2)
with the latest Xcas. You can get your solution with c_2=1.
You are missing y=x with your general solution.

thank you!
I'll try, hoping in the future to have the XCas feature also in the Prime...


(I wonder if there is a regular version of XCas that run into Mac OS X (without Windows emulator): I need it...)
EDIT: found! http://www-fourier.ujf-grenoble.fr/~pari...all_en#osx

[parisse]

There are native versions of Giac/Xcas for the 3 major desktop OS: windows, linux and mac. Giac is also ported to pure javascript code (embeddable into a web application), android (Xcas pad UI) and all TI nspire up to OS 3.9 (khicas, run also on non-CAS models). For ios, there is no free port I know, pocketcas is using giac as math kernel.

[salvomic]

(05-02-2015 12:43 PM)parisse Wrote:  There are native versions of Giac/Xcas for the 3 major desktop OS: windows, linux and mac. Giac is also ported to pure javascript code (embeddable into a web application), android (Xcas pad UI) and all TI nspire up to OS 3.9 (khicas, run also on non-CAS models). For ios, there is no free port I know, pocketcas is using giac as math kernel.

well :-)
I hope to have also an iOS version too (for my iPhone), paid or not!

Installed just now the Mac OS X version (unstable).
Trying the ODE I get an error (see image): have I missed something in syntax?

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...
And the 64bit files seem not to be an image (dmg for Mac)...
Can you kindly help me, thank you?

Salvo

[salvomic]

...I'm trying Pocket CAS in iOS (iPad): very impressive.

However the ODE y'=(x+y)^2 isn't solved also there...

[Tugdual]

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.