# Thread: differential equation with differential input

1. ## 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

2. ## Re: differential equation with differential input

Originally Posted by mopen80
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

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.