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Absurdly Off Topic: Any math majors/Profs out there?

 
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eric

Since 13 Jan 2006
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PostSun Jan 27, 19 1:21 pm    Absurdly Off Topic: Any math majors/Profs out there? Reply with quote

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. On-line 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

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Last edited by eric on Sun Jan 27, 19 1:54 pm; edited 1 time in total

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jasonq

Since 12 Jan 2009
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vancouver
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PostSun Jan 27, 19 1:44 pm     Reply with quote

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 little-ish 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.

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wylieflyote

Since 30 Jun 2006
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Puget Sound & Wa. Coast
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PostSun Jan 27, 19 4:55 pm     Reply with quote

Are boardshorts over a wetsuit still cool?
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Kip Wylie

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consumer

Since 28 Nov 2010
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PostSun Jan 27, 19 6:56 pm     Reply with quote

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)/x-v(1+v+v^2)]/x = 0

[v(v+1-1-v-v^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.

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eric

Since 13 Jan 2006
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PostSun Jan 27, 19 7:17 pm     Reply with quote

Yeah, V is a variable.
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1surfer

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PostFri Feb 01, 19 2:22 pm    XXOO Reply with quote

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scottm

Since 12 Jun 2006
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PostSat Feb 02, 19 1:51 pm     Reply with quote

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...

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undertow

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PostWed Feb 06, 19 2:20 pm     Reply with quote

Fallout 76 is a great game!!!!!

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