#math - Tue 10 Apr 2007 between 00:00 and 00:13

NY Lost Funds



ailndxah ok
Pigeon`the system is x' = 3*(x + y - (1/3)*x^3 - k) and y' = -(1/3)*(x + 0.8*y - 0.7)
so i already put the = 0
JabberWalkieoh, well that was confusing me..
just solve for x and y
% Solve[ { 3*(x + y - (1/3)*x^3 - k) == 0, -(1/3)*(x + 0.8*y - 0.7) == 0},{x,y}]
mbotJabberWalkie: {{y -> 0.125*(7. + 75.59526299369237/(36288. - 41472.*k + 41472.*Sqrt[0.7725694444444444 - 1.75*k + 1.*k^2])^(1/3) - 0.33070855249337494*(36288. - 41472.*k + 41472.*Sqrt[0.77256944444444
44 - 1.75*k + 1.*k^2])^(1/3)), x -> -7.559526299369238/(36288. - 41472.*k + 41472.*Sqrt[0.7725694444444444 - 1.75*k + 1.*k^2])^(1/3) + 0.03307085524933749*(36288. - 41472.*k + 41472.*Sqrt[0.7725694444
444444 - 1.75*k + 1.*k^2])^(1/3)}, {y -> 0.125*(7. - (37.797631496846186 + 65.46741815830327*I)/(36288. - 41472.*k + 41472.*Sqrt[0.7725694444444444 - 1.75*k + 1.*k^2])^(1/3) + (0.16535427624668747 -
0.2864020077080422*I)*(36288. - 41472.*k + 41472.*Sqrt[0.7725694444444444 - 1.75*k + 1.*k^2])^(1/3)), x -> (3.779763149684619 + 6.546741815830327*I)/(36288. - 41472.*k + 41472.*Sqrt[0.7725694444444444
- 1.75*k + 1.*k^2])^(1/3) - (0.016535427624668746 - 0.02864020077080422*I)*(36288. - 41472.*k + 41472.*Sqrt[0.7725694444444444 - 1.75*k + 1.*k^2])^(1/3)}, {y -> 0.125*(7. - (37.797631496846186 - 65.
[3 @more lines]
Pigeon`i know but...
:P
JabberWalkiethere...
seems a little messy..
Pigeon`: perhaps just put the system of equations in matrix form, and show its determinate is nonzero for any value of k
err
nm..
non-linear :S
Pigeon`but i got an x^3
JabberWalkieok, well take -(1/3)*(x + 0.8*y - 0.7) == 0, solve for y and sub into the other equation, its odd powerd in x^3, so it has to have a real zero somewhere
Pigeon`thats what i did first
-1/3*x^3 - 0.25*x + 0.875 - k = 0
JabberWalkiePigeon`: you just need to show the existance of such a point, we dont need to know what it is
Pigeon`yea
bkudriacan someone help me understand how to do recursive addition? all the definitions i see online are: add(n,0) = n, and add(s(n),m) = s(add(n, m)), where s is the successor function. i understand this, but i need to define add(n,m), not add(s(n),m), and i only can use the successor function.
ailndxfor y = f(x) do you say that x is independent and y dependant?
Pigeon`ok so i say, there will be 1 real solution cuz its an odd power
JabberWalkieyeah
Pigeon`and to proove that it got only one..
JabberWalkieonly one?
Pigeon`i used mathematica and i saw only 1 real solution! :P
well only 1 real solution
not 3 real solution
JabberWalkiei thought you needed to show there was at least one critical point, not that there was only one critical point...
for some values of k, you might have more that one critical point...i dont really see that holding...
kercyrPigeon`, look at the function -1/3*x^3 - 0.25*x + 0.875 - k. Does it increase anywhere?
Pigeon`increase?
well no

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