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[0.77256944444444 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 |

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 k err nm.. 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! :P well only 1 real solution not 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 |