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Math Help - Second-Order Differential Equations

  1. #1
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    Second-Order Differential Equations

    A series circuit contains a resistor with R = 24 , an inductor with L = 2 H, a capacitor with C = 0.005 F, and a 12 V battery. The initial charge is Q = 0.001 C and the initial current is 0
    I have to find the charge at time t

    I know how to do the problem if it equaled a function but it just equals 12..i'm confused?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Jessica11 View Post
    A series circuit contains a resistor with R = 24 , an inductor with L = 2 H, a capacitor with C = 0.005 F, and a 12 V battery. The initial charge is Q = 0.001 C and the initial current is 0
    I have to find the charge at time t

    I know how to do the problem if it equaled a function but it just equals 12..i'm confused?
    You should have a second order linear constant coefficient non-homogeneous ODE for q, it is of the form:

    q''+Aq'+Bq=v(t)

    where v(t)=12, and q(0)=0.001, q'(0)=0.

    Now this is a bog standard IVP

    CB
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  3. #3
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    f(x)= 12 is a function! It is a constant function. That just makes this problem easier than if it were a more complicated function.
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