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Please Help me Split this Equation into 2 equations

  1. Aug 21, 2005 #1
    Im trying to turn this equation into 2 seperate equations in order to place it in a runge kutta problem. This is the proposed problem and conditions:

    [tex]\frac{d^2f}{dx^2} + f = 0[/tex]

    allowing

    [tex]f (x) = A\cos x + B\sin x[/tex]
    [tex]f ' (x) = -A\sin x + B\cos x[/tex]
    [tex]f '' (x) = -A\cos x - B\sin x[/tex]

    and
    [tex]g = \frac{df}{dx}[/tex]

    meaning
    [tex]\frac{df}{dx} - g = 0[/tex] which is identical to [tex]\frac{d^2f}{dx^2} + f = 0[/tex]

    so
    [tex]\frac{dg}{dx} + f = 0[/tex]

    the initial conditions for equation 1 are:
    [tex]f (0) = 1[/tex]
    [tex]f ' (0) = 0[/tex]

    and for equation 2 are:
    [tex]f (0) = 0[/tex]
    [tex]g (0) = 1[/tex]

    I hope this formatting is more easy to read.
    any suggestions??
     
    Last edited: Aug 21, 2005
  2. jcsd
  3. Aug 21, 2005 #2

    Zurtex

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    Right, you really need to learn Latex. So your post I tjink would go like this:

    [tex]\frac{d''f}{dx''} + f = 0[/tex]

    Therefore:

    [tex]f (x) = A\cos x + B\sin x[/tex]
    [tex]f ' (x) = -A\sin x + B\cos x[/tex]
    [tex]f '' (x) = -A\cos x - B\sin x[/tex]

    However, before I try to translate the rest, I feel it worth noting that this is very confusing:

    [tex]\frac{d''f}{dx''}[/tex]

    Please stick to something like this:

    [tex]\frac{d^{2}y}{dx^{2}} \quad \text{or} \quad y''[/tex]
     
  4. Aug 21, 2005 #3
    yes, that is correct.

    Off Subject, but what is latex?

    Please continue your help.
     
  5. Aug 21, 2005 #4

    Zurtex

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    https://www.physicsforums.com/showthread.php?t=8997

    Click on any of my equtions and a box should appear showing the cde I used to write it.

    It's very early in the morning here, I'll come back and look at your problem later sorry, too tired right now.
     
  6. Aug 21, 2005 #5
    Ok, well, I have changed the formatting, thank you for your continued help, ill check back in in the morning. Thanks again.

    Im just looking for the 2 equations to plug into the runge kutta 4. I hope you can help. I have another post with my C++ code in it, but the code is correct. I just have to do this to show my professor.
     
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