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Math Help - First Order Linear Diff. Eqn?

  1. #1
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    First Order Linear Diff. Eqn?

    Hi all,

    I am unsure of what to do with this one.

    I have been given some conditions in an electric circuit. Due to Kirchoff's law I have calculated the differential equation to be:

    2(dI/dt) + 12(dQ/dt) + 10Q = 12 sin(t)

    where 12 sin(t) is the supplied voltage.

    Im supposed to find Q at time t with initial conditions Q(0) = 0.2 and I(0)=0.

    Is this a first order linear differential equation? Or is it classified as something else?

    What confuses me is that it has 2(dI/dt) + 12(dQ/dt). I was thinking that perhaps dI/dt = d^2Q/dt^2 or vise versa but really im not sure.
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  2. #2
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    Actually yes,

    dI/dt = d^2Q/dt^2

    so the equation is

    2(d^2Q/dt^2) + 12(dQ/dt) + 10Q = 12 sin(t)

    which is a second order linear differential equation.
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  3. #3
    Behold, the power of SARDINES!
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    [quote=woody198403;148103]Actually yes,

    dI/dt = d^2Q/dt^2

    so the equation is

    2(d^2Q/dt^2) + 12(dQ/dt) + 10Q = 12 sin(t)

    This is a 2nd order linear DE

    So first we need to solve the associated homogenious equation

    2Q''+12Q'+10Q=0

    2m^2+12m+10=0 \iff 2(m+1)(m+5)=0

    so the two roots are m=-1 and m=-5

    This gives the complimentry solution y=c_1e^{-t}+c_2e^{-5t}

    Now we need to find the particular solution

    since the driving function is 12sin(t)

    we know the particular solution is of the form

    y=A\sin(t)+B\cos(t)

    taking a few derivatives and plugging into the non homogenious equation and solvinf for A and B will finish the problem.

    Good luck.
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by woody198403 View Post
    Hi all,

    I am unsure of what to do with this one.

    I have been given some conditions in an electric circuit. Due to Kirchoff's law I have calculated the differential equation to be:

    2(dI/dt) + 12(dQ/dt) + 10Q = 12 sin(t)

    where 12 sin(t) is the supplied voltage.

    Im supposed to find Q at time t with initial conditions Q(0) = 0.2 and I(0)=0.

    Is this a first order linear differential equation? Or is it classified as something else?

    What confuses me is that it has 2(dI/dt) + 12(dQ/dt). I was thinking that perhaps dI/dt = d^2Q/dt^2 or vise versa but really im not sure.
    Someone asked a question very similar to yours: Click here to go the thread.

    I have it worked out.
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