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Finding derivatives for second order differential equation

  1. Oct 3, 2011 #1
    1. The problem statement, all variables and given/known data


    My first post here

    I have a numerical problem for Matlab but I get stuck with the basic math...

    For a circuit I have three equations:

    1.Inductance: L=Lo/(1+I^2)
    2.Voltage over the inductance: V=L*dI/dt
    3.Current over a condensator: I=-C*dV/dt

    2. Relevant equations
    From this I should be able to derive the second order differential equation:

    4. d2/dt2=2I(dI/dt)^2/(1+I^2)-I(1+I^2)/Lo*C

    I know I must find the derivative for V, dV/dt and substitute this into I=-C*dV/dt and this should yield equation 4 but I think my derivatives are all wrong!

    3. The attempt at a solution
    Basically I need help to use the chain rule (i guess?) and finding the derivative for V=L*dI/dt

    This is what I got: dV/dt=dI/dt*(-Lo*2I)/(1+I^2)^2+L*d2/dt2*??? something is wrong...

    Would really appreciate the help!
    Last edited by a moderator: Oct 3, 2011
  2. jcsd
  3. Oct 3, 2011 #2


    Staff: Mentor

    That's condenser, not condensator. Condensers are usually called capacitors nowadays.

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