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Homework Help: Eliminating a variable from system of ODE's

  1. May 10, 2010 #1
    1. The problem statement, all variables and given/known data

    Project 1.jpg The writing below the equation is the correct order of the constants directly above it.

    3. The attempt at a solution

    [tex]
    h=\frac{-g\prime-a_1g+E(t)}{a_2}
    [/tex]

    So I solved for h in the dg/dt equation, and plug this into the h in the dh/dt equation. My question is where do I go from here to satisfy the relation given in the problem above.
     
    Last edited: May 10, 2010
  2. jcsd
  3. May 10, 2010 #2

    vela

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    Now you want to differentiate your expression for h and plug that result into the LHS of the dh/dt equation to get everything in terms of g and its derivatives.
     
  4. May 11, 2010 #3
    So [tex]
    h=\frac{-g\prime-a_1g+E(t)}{a_2}
    [/tex]

    becomes

    [tex]
    h\prime=-g\prime\prime-g\prime+E\prime(t)
    [/tex]

    which replaces dh/dt in the original equation?
     
  5. May 11, 2010 #4

    vela

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    You made a few mistakes. What happened to a1 and a2?
     
  6. May 11, 2010 #5
    sorry, still trying to get used to latex

    [tex]h\prime=\frac{-g\prime\prime-a_1g\prime+E\prime(t)}{a_2}[/tex]

    So this result replaces the left hand side of the dh/dt equation in the original system.

    Also, dg/dt from the original equation [tex]dg/dt=-a_1g-a_2h+E(t)[/tex]
    becomes

    [tex]g\prime\prime=-a_1g\prime-a_2h\prime+E\prime[/tex]

    and plug in dh/dt into this equation, making

    [tex]g\prime\prime=-a_1g\prime-a_2(-a_3g+a_4h)+E\prime[/tex]
     
    Last edited: May 11, 2010
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