Awkward diff. eq., advice appreciated

[gstqtfr]

Hi,

I've got an awkward diff. eq. i'd really appreciate any help i can get with.

the DE is

y' = x - xy -y

in latex, it's

\frac{dy}{dt} & = & Cx - Dxy - Ey

but ignore the constants ...

it looked as though this would be easy to do with separation of variables at first, but couldn't work it out that way ... couldn't think of an integrationg factor ... it looks easy, but i seem to have a block on this, can't see a way ot get it into some useful form or find somehting to substitute that would make it come out ok ...

any ideas?

 

[dextercioby]

Do you know how to solve an equations such as

\frac{dy}{dx}+f(x) y= g(x)

? In other words, do you know what an integrating factor is ?

Daniel.

 

[gstqtfr]

Hi Daniel,

Yes, I know what an IF is, but can't see an obvious one for this (i get the distinct feeling that there is one, but I'm damned if i can see it at the moment!)

one thing i didn't make at all clear when i posted the prob. is that we have

y'(t) = x - xy -y

apologies, it needs to be solved w.r.t. t

any suggestions on a suitable IF?

 

[gstqtfr]

help me out here, guys. am i missing anything mind-bogglingly obvious, such as an easy integrating factor, or is this actually a problem that requires something else? if anybody who vies this problem also can't see an obvious solution, let me know, will you? otherwise i'll think I'm just going nuts/suffering from advanced decripitude ...

 

[arunbg]

hello gstqtfr

By y'(t) do you mean \frac{dy}{dt} ? Is x also a function of t and given in the question ? The question really isn't very clear. Can you post the question in its entire form ?

 

[gstqtfr]

Hi Arunbg,

Apologies, isn't clear at all, is it? BTW, 1st-time on this forum, can you post latex on here? anyway, the problem in 'tex is

\frac{dy}{dt} = Cx - Dxy - Ey

& both x and y are functions of t. this is why I'm finding this difficult to solve, i guess; if it were a case of

\frac{dy}{dx} = x - xy -y

(constants elided for clarity), then it's easy enough to separate the variables, for example. However, I can't see a way of doing this, since we have x(t) & y(t).

Any ideas? I'm really pretty stuck here ...

 

[dextercioby]

In the way you imply it, it's ODE with 2 unknown functions. So it can't be really solved. I mean, determine BOTH x=x(t) and y=y(t) from the ODE.

Daniel.

 

[gstqtfr]

Hi Daniel,

Thanks for the reply, sorry I took so long to respond, I've been afk quite a bit today ...

Good! So it can't be solved through some trick I didn't know about. That's a relief - I was wondering whether there was some special technique I didn't know about (maybe related to PDEs, about which I know very little) that could be used.

Now I can get on to do some numerical integration, looking for steady states, etc.

Thanks for your help, guys!