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

### NY Lost Funds

 ailndx ah 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 JabberWalkie oh, 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}] mbot JabberWalkie: {{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[0.7725694444444444 - 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[0.7725694444444444 - 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 JabberWalkie there...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 kerrnm..non-linear :S Pigeon` but i got an x^3 JabberWalkie ok, 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 JabberWalkie Pigeon`: you just need to show the existance of such a point, we dont need to know what it is Pigeon` yea bkudria can 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. ailndx for 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 JabberWalkie yeah Pigeon` and to proove that it got only one.. JabberWalkie only one? Pigeon` i used mathematica and i saw only 1 real solution! :Pwell only 1 real solutionnot 3 real solution JabberWalkie i 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... kercyr Pigeon`, look at the function -1/3*x^3 - 0.25*x + 0.875 - k. Does it increase anywhere? Pigeon` increase?well no