Question

Pllllllease someone help :(
FInd the general solution to

dx/dt= 2x(1 − x/3) − xy
dy/dt= −2y + 3xy

Answer 1

if you can help me i'll love you forever .. i'm so stuck

Answer 2

i think that all you do is find x=x(t) and y=y(t) for each but i dont know how!

Answer 3

do you think you can help me :(

Answer 4

It's simple without the last term xy, so I'm thinking!

Answer 5

ok thank you .. i'm thinking that you solve and just keep one as a constant? i'm not sure.

Answer 6

like the variable that your not solving for of course

Answer 7

this assignemnt is due tm morning and if i dont do it i'm soo screwed but I'm seriously so confused!

Answer 8

Is it familiar, as your lecture?

Answer 9

not relaly to be honest

Answer 10

Do you have any link for similar problem?

Answer 11

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

Answer 12

i'm trying to figure it out using those .. did you get those links? it said i lost connection

Answer 13

I did, my PC fluctuate all the time. I'm reading!

Answer 14

ok, its like a combination of both it seems .. i'm not sure if i know what i'm doing..

Answer 15

do you understand it at all?

Answer 16

Nope! I'm getting help from other, see if it works (sighs)

Answer 17

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

Answer 18

2x(1 − x/3) − xy = 0
−2y + 3xy = 0
-> y ( -2 + 3x) = 0
=> y = 0, x = 2/3

Answer 19

Look like we solving system of equation by substitution:

Answer 20

Replace y = 0 and x = 2/3 into (1)

Answer 21

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?

Answer 22

we have y = 0 and x = 2/3 to plug into:
2x(1 − x/3) − xy = 0 (1)

Answer 23

ok thanks!

Answer 24

You figure it out?

Answer 25

yes i did! thank you!

Answer 26

y = 0 --> x = 0, x = 3

Answer 27

2 intersection points ( 0, 0 ) and ( 3, 0)

Answer 28

With x = 2/3 --> y = 14/9

Answer 29

point ( 2/3, 14/9)

Answer 30

So we have 3 solutions !

Answer 31

Do you think we're fine here?

Answer 32

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?

Answer 33

Of course :P
One at the time x = 2/3 or y = 0

Answer 34

So the whole concept is find intersection points

Answer 35

but if its a dx/dt and then a dy/dt can we do that? ahhh ok ok!

Answer 36

factor x, y out, then set = 0 --> x, y value from one equation.

Answer 37

use it value to substitude into the other equation.

Answer 38

ah ok ok!

Answer 39

Happy :)

Answer 40

Sarah ???

Answer 41

ahah yes1 thank you!!!

Answer 42

Finally ( relieve sighs)

Answer 43

ahah sorry i was such a pain in the retrice

Answer 44

You need to organize your notes

Answer 45

Good thing is you have it to show me, so I figure out the whole idea is find intersection points

Answer 46

Otherwise I don't even know what you want me to do !

Answer 47

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!

Answer 48

I'm really exhausted today!

Answer 49

Just post up to see if others better!

Answer 50

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.

Answer 51

or if you even tell me how ..

Answer 52

Then I need some sample as you did show me!

Answer 53

its just for the DE above, the first ones we were working with!

Answer 54

Ok!

Answer 55

dx/dt= 2x(1 − x/3) − xy

Answer 56

yes!

Answer 57

Now what to do?

Answer 58

i'm not sure how to find where its increasing and decreasing

Answer 59

Let me search internet, look like need second direvative

Answer 60

hhah awe, no dont worry about it! i'lll just leave it blank! go to sleep!

Answer 61

It says, all we'll do is plug it the other value around (0,0) and (3,0) to get the signs

Answer 62

suppose (1,0) or ( 0,1)

Answer 63

hmm.

Answer 64

wish i understood this stuff, ok i'm just going to make something up.

Answer 65

It's not difficult, just plug value around max,min.

Answer 66

so its increasing if dy/dt<0 ?
and decreasing if dx/dt<0?

Answer 67

Yep

Answer 68

really! wow, i just guessed.

Answer 69

You got it,
At (1,0) , equation = 4/3 >0 => decreasing!

Answer 70

awesome! thanks so much for all your help! i really appreciate it! would have died without ya! :)

Answer 71

I did hear it from a guy today, I'm proud that I save couple of lives daily :P

Answer 72

What time from your area now?

Answer 73

its 12:33 am

Answer 74

Oh same here!

Answer 75

ahah then get some rest :)
night!!

Answer 76

What grade are you?