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Math Help - Characteristics of an equation

  1. #1
    Junior Member
    Joined
    Oct 2009
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    31

    Characteristics of an equation

    How do I calculate the slope of an equation if I don't have any initial data?

    du/dt + (1/2 * (1 + u)^2) = 0

    The slope is therefore

    dx/dt = a(u) = f'(u) = 1 + u

    With no initial data how do I calculate u(x,t)?
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  2. #2
    Member
    Joined
    Dec 2009
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    Solve for slope without data?

    Calculating anything without initial data is veeeeeery troublesome =)

    du/dt + 1/2*(1+u)^2 = 0

    du/dt+ 1/2*(1^2+2u+u^2) = 0

    du/dt +1/2 + u + u^2 = 0

    du/dt + u = -u^2 - 1/2 this gives you ke^-x

    Set
    u = ax^2 + bx + c gives you uŽ= 2ax +b

    2ax +b +ax^2 +bx +c = -u^2 -1/2 gives you a = -1
     <br /> <br />
2ax +bx = 2*(-1) +b = 0<br />
b = 2

    b + c = -1/2 gives you c = -2,5

    U = Ke^(-x) -x^2 +2x -2.5

    To determine K, I think you need a value somewhere,
    If you plot that graph for different values of K you will see that the slopes have different angles exept for the x value for maximum/minimum point, is that the value you are trying to find? Otherwise you need some initial data to determine K. ( I think)
    hope it was somewhat helpful.
    Last edited by Henryt999; January 9th 2010 at 02:47 PM.
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