anonymous
  • anonymous
Pllllllease someone help :( FInd the general solution to dx/dt= 2x(1 − x/3) − xy dy/dt= −2y + 3xy
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
if you can help me i'll love you forever .. i'm so stuck
anonymous
  • anonymous
i think that all you do is find x=x(t) and y=y(t) for each but i dont know how!
anonymous
  • anonymous
do you think you can help me :(

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anonymous
  • anonymous
It's simple without the last term xy, so I'm thinking!
anonymous
  • anonymous
ok thank you .. i'm thinking that you solve and just keep one as a constant? i'm not sure.
anonymous
  • anonymous
like the variable that your not solving for of course
anonymous
  • anonymous
this assignemnt is due tm morning and if i dont do it i'm soo screwed but I'm seriously so confused!
anonymous
  • anonymous
Is it familiar, as your lecture?
anonymous
  • anonymous
not relaly to be honest
anonymous
  • anonymous
Do you have any link for similar problem?
anonymous
  • anonymous
one sec... http://www.mast.queensu.ca/~math232/2012slides/slides2012-16/page02.jpg http://www.mast.queensu.ca/~math232/2012slides/slides2012-16/page03.jpg http://www.mast.queensu.ca/~math232/2012slides/slides2012-16/page04.jpg http://www.mast.queensu.ca/~math232/2012slides/slides2012-16/page05.jpg
anonymous
  • anonymous
i'm trying to figure it out using those .. did you get those links? it said i lost connection
anonymous
  • anonymous
I did, my PC fluctuate all the time. I'm reading!
anonymous
  • anonymous
ok, its like a combination of both it seems .. i'm not sure if i know what i'm doing..
anonymous
  • anonymous
do you understand it at all?
anonymous
  • anonymous
Nope! I'm getting help from other, see if it works (sighs)
anonymous
  • anonymous
i just dont understand becuase its mixing the 2 ideas .. so i dont know if i'm supposed to try and combine it or, .. i suck
anonymous
  • anonymous
2x(1 − x/3) − xy = 0 −2y + 3xy = 0 -> y ( -2 + 3x) = 0 => y = 0, x = 2/3
anonymous
  • anonymous
Look like we solving system of equation by substitution:
anonymous
  • anonymous
Replace y = 0 and x = 2/3 into (1)
anonymous
  • anonymous
is that what were supposed to do? or are we only supposed to sub y=0 into the other one since in that equation were not solving for x at all?
anonymous
  • anonymous
we have y = 0 and x = 2/3 to plug into: 2x(1 − x/3) − xy = 0 (1)
anonymous
  • anonymous
ok thanks!
anonymous
  • anonymous
You figure it out?
anonymous
  • anonymous
yes i did! thank you!
anonymous
  • anonymous
y = 0 --> x = 0, x = 3
anonymous
  • anonymous
2 intersection points ( 0, 0 ) and ( 3, 0)
anonymous
  • anonymous
With x = 2/3 --> y = 14/9
anonymous
  • anonymous
point ( 2/3, 14/9)
anonymous
  • anonymous
So we have 3 solutions !
anonymous
  • anonymous
Do you think we're fine here?
anonymous
  • anonymous
how did you get (3,0) ? ok .. but since in each case your solving for one variable, you cant sub in both an x and a y into the first equation can you? like doesn't that not make sense?
anonymous
  • anonymous
Of course :P One at the time x = 2/3 or y = 0
anonymous
  • anonymous
So the whole concept is find intersection points
anonymous
  • anonymous
but if its a dx/dt and then a dy/dt can we do that? ahhh ok ok!
anonymous
  • anonymous
factor x, y out, then set = 0 --> x, y value from one equation.
anonymous
  • anonymous
use it value to substitude into the other equation.
anonymous
  • anonymous
ah ok ok!
anonymous
  • anonymous
Happy :)
anonymous
  • anonymous
Sarah ???
anonymous
  • anonymous
ahah yes1 thank you!!!
anonymous
  • anonymous
Finally ( relieve sighs)
anonymous
  • anonymous
ahah sorry i was such a pain in the retrice
anonymous
  • anonymous
You need to organize your notes
anonymous
  • anonymous
Good thing is you have it to show me, so I figure out the whole idea is find intersection points
anonymous
  • anonymous
Otherwise I don't even know what you want me to do !
anonymous
  • anonymous
ahah i know i know .. i'm slacking a bit i'll admit, but totally appreciate you helping me .. want to help me with one more thing :) ? LAST thing i promise!
anonymous
  • anonymous
I'm really exhausted today!
anonymous
  • anonymous
Just post up to see if others better!
anonymous
  • anonymous
PLEASE :) its just a little one From the differential equations determine (for x > 0, y > 0) where x and y are decreasing and where they are increasing.
anonymous
  • anonymous
or if you even tell me how ..
anonymous
  • anonymous
Then I need some sample as you did show me!
anonymous
  • anonymous
its just for the DE above, the first ones we were working with!
anonymous
  • anonymous
Ok!
anonymous
  • anonymous
dx/dt= 2x(1 − x/3) − xy
anonymous
  • anonymous
yes!
anonymous
  • anonymous
Now what to do?
anonymous
  • anonymous
i'm not sure how to find where its increasing and decreasing
anonymous
  • anonymous
Let me search internet, look like need second direvative
anonymous
  • anonymous
hhah awe, no dont worry about it! i'lll just leave it blank! go to sleep!
anonymous
  • anonymous
It says, all we'll do is plug it the other value around (0,0) and (3,0) to get the signs
anonymous
  • anonymous
suppose (1,0) or ( 0,1)
anonymous
  • anonymous
hmm.
anonymous
  • anonymous
wish i understood this stuff, ok i'm just going to make something up.
anonymous
  • anonymous
It's not difficult, just plug value around max,min.
anonymous
  • anonymous
so its increasing if dy/dt<0 ? and decreasing if dx/dt<0?
anonymous
  • anonymous
Yep
anonymous
  • anonymous
really! wow, i just guessed.
anonymous
  • anonymous
You got it, At (1,0) , equation = 4/3 >0 => decreasing!
anonymous
  • anonymous
awesome! thanks so much for all your help! i really appreciate it! would have died without ya! :)
anonymous
  • anonymous
I did hear it from a guy today, I'm proud that I save couple of lives daily :P
anonymous
  • anonymous
What time from your area now?
anonymous
  • anonymous
its 12:33 am
anonymous
  • anonymous
Oh same here!
anonymous
  • anonymous
ahah then get some rest :) night!!
anonymous
  • anonymous
What grade are you?

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