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Math Help - Convert the Second Order Equation

  1. #1
    Len
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    Convert the Second Order Equation

    Convert the second order equation

    \frac{d^2y}{dt^2}=0

    into a first order system using:

    v=\frac{dy}{dt}

    Then find the general solution for \frac{dv}{dt} equation then sub the solution into the \frac{dy}{dt} equation and find the solution of the system.

    ------------

    I'm not really sure with this but


    \frac{dy}{dt}=v , \frac{dv}{dt}=0

    so y(t)=k_1*e^t, v(t)=k_2

    Then I have no idea. Some help would be very appreciated.
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  2. #2
    MHF Contributor Calculus26's Avatar
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    you are correct in that dv/dt = 0

    v = k1

    Then


    v = dy/dt = k1

    y = k1 *t + k2
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  3. #3
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    Quote Originally Posted by Len View Post
    Then find the general solution for \frac{dv}{dt} equation
    \frac{dv}{dt} = 0

    the solution is v(t) = C_1

    then sub the solution into the \frac{dy}{dt} equation and find the solution of the system.
    \frac{dy}{dt} = v(t) = C_1

    ~dy = C_1 ~dt

    y(t) = C_1t + C_2
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