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Math Help - differential equation with differential input

  1. #1
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    differential equation with differential input

    Hi All,

    I have that differential equation that model some mechanical system, but i am confused how to call it:

    tau*(dy/dt)+y=tau*k*(dx/dt)+x

    tau =R*C time constant of the system.

    my question is , how to call this equation with the term dx/dt exist. Also how to simulate it using RC electric circuit. Any idea?

    Also if the initial condition is known, does this equation has an exact solution.

    Any help is appreciated as i have been struggling with this for long time.

    mopen
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  2. #2
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    Re: differential equation with differential input

    Quote Originally Posted by mopen80 View Post
    Hi All,

    I have that differential equation that model some mechanical system, but i am confused how to call it:

    tau*(dy/dt)+y=tau*k*(dx/dt)+x

    tau =R*C time constant of the system.

    my question is , how to call this equation with the term dx/dt exist. Also how to simulate it using RC electric circuit. Any idea?

    Also if the initial condition is known, does this equation has an exact solution.

    Any help is appreciated as i have been struggling with this for long time.

    mopen
    I think you are confused because you think you must solve for $x(t)$

    $x(t)$ is a portion of the driving function and will be specified.

    What you have is this

    differential equation with differential input-clipboard01.jpg

    where $h(t)$ is the plant response generated by your differential equation.

    assuming $x(t)$ is a voltage signal $k \tau \dot{x}$ can be generated with a capacitor and an gain component such as an op amp.
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