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eric
Since 13 Jan 2006
1400 Posts
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Sun Jan 27, 19 1:21 pm Absurdly Off Topic: Any math majors/Profs out there? 


Doing a self study ODE course. Fun stuff, and for the most part smooth sailing.
I have three problems that are giving me fits, one of which is below. Online ODE calculators do numerical analysis, whereas I need a solution done in exact form. I am many hours in, and keep ending up with a nasty integral, that seems to defy any attempts at an exact solution.
Here is the original problem from Stroud DE page 39:
y(xy+1) +x(1+xy+x^2y^2)(dy/dx) = 0 Let y = v/x
"Transformations. Make the given substitution and use methods of first order homogeneous equations"
I know how to do substitutions, Bernoulli, and use an Integrating Factor. We are not supposed to apply any numerical/ La Place method at this point. I have been treating this as a Separable DE post substitution. I feel like I am not seeing something obvious.
Long shot to post this here, but why not!?
Thanks,
Eric _________________ I only kite if I am alone, or with somebody else.
https://www.wildwoodacademy.org/
GO BEARS! Last edited by eric on Sun Jan 27, 19 1:54 pm; edited 1 time in total 


jasonq
Since 12 Jan 2009
169 Posts
vancouver
Stoked

Sun Jan 27, 19 1:44 pm 


i am neither, and a many, many years away from DE classes.
that said, mathematica can almost certainly deal with the problem using symbolic math, not numerical methods (unless you want it to). I rely on mathematica so much, i am not sure i can do addition by hand anymore.
a mathematica license is $$$ but a littleish known fact is that the Raspbian OS for the Raspberry Pi includes a free copy of mathematica. For about $50 total for a RB Pi 3B+ and an SD Card you can run it to your heart's content.
I think but am not sure there is a way to get wolfram alpha to do it to via a web browser. 


wylieflyote
Since 30 Jun 2006
1369 Posts
Puget Sound & Wa. Coast
XTreme Poster

Sun Jan 27, 19 4:55 pm 


Are boardshorts over a wetsuit still cool? _________________ CGKA Member

Kip Wylie 


consumer
Since 28 Nov 2010
396 Posts
banned
Obsessed

Sun Jan 27, 19 6:56 pm 


y(xy+1) +x(1+xy+x^2y^2)(dy/dx) = 0 Let y = v/x
is v a variable?
if not then dy/dx = v/x^2
v/x(x*v/x+1)+x(1+x*v/x+x^2(v/x)^2)*(v/x^2)=0
v/x(v+1)+x(1+v+v^2)(v/x^2)=0
v/x(v+1)+(1+v+v^2)(v/x)=0
[v(v+1)/xv(1+v+v^2)]/x = 0
[v(v+11vv^2)]/x=0
v^3/x=0
um lol v=0 or x = infinity
obviously i'm missing something too.
if v is a variable then dy/dx = v/x2 + dv/xdx
and is now out of my pay grade. good luck. 


eric
Since 13 Jan 2006
1400 Posts
XTreme Poster



1surfer
Since 20 Apr 2010
333 Posts
'Ualapu'e / High Rockies
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Fri Feb 01, 19 2:22 pm XXOO 


XXX OOO = hugs and kisses _________________ Ozone Reo's. C&k Beach Boy Service, Windsurfing Waikiki, Hawaiian Windriders, NSRN. 


scottm
Since 12 Jun 2006
90 Posts

Sat Feb 02, 19 1:51 pm 


Board shorts over a full wetsuit never were cool, and never will be cool. And failing to define V as a third variable, makes your professor, somebody who would wear board shorts over a wetsuit. But that was probably one of the unstated assumptions... 


undertow
Since 15 Feb 2008
350 Posts
BeaversBurg
Obsessed

Wed Feb 06, 19 2:20 pm 


Fallout 76 is a great game!!!!! 


