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Math Help - 4 differencial equations problem

  1. #1
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    4 differencial equations problem

    P1. Find equilibrium pts. of model:

    [da/dt] = [1a + 3b + 5]
    [db/dt] [2a + 4b + 6]

    P2. Find equilibrium pts. of model:

    [da/dt] = [a - b]
    [db/dt] [2a - b - (a^2)]

    P3. Find equilibrium of this z(t) @ time t:

    dz/dt = A - cB(((2D)/(BE))^(3/4))(z^(3/4)) (c is a constant)

    P4. Linearize this model/equation and use least-squares fit (w/ given points) to estimate constants:

    dz/dt = az - ab(z^2)

    t : 0 1 2 3 4 5
    z : 1.0 1.2 1.4 1.6 1.8 2.0

    Good luck and tenx!
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  2. #2
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    Joined
    Nov 2006
    Posts
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    P1. Put both derivatives =0 and subtract 2 times the first equation from the second to get an equation with only b. Then solve for b and use the result to find a.

    P2. Again, both derivatives =0. The first equation becomes a=b. That result transforms the second equation into an equation with only one variable. Solve it.

    P3. I'm assuming that A, B, D and E are also constants? Just put that expression =0 and solve for z(t).

    P4. Again, the equation is "what you wrote"=0. Just divide both sides with z to simplify the equation.

    If you want more help than that, I think you should show us what you've got so far.
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