1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    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

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook