Understanding Differential Equations: Exploring Relations between Functions

[tomizzo]

Hello,

I have a question that is relevant to differential equations. Say for example I have two functions that are related to one anothers derivatives. For example, the voltage acrossed an inductor is proportional to the rate of change of current through that inductor.

My question for you is, what exactly is the terminolgy for something like this? In the most general form, it is relation between two functions. But would you classify this as a differential equation? I had thought that differential equations are restricted to only relating derivatives of the same function.

So I suppose in my example case, if I were to feed a specific voltage across the inductor, I would eliminate the arbitrary voltage function would allow the relationship to be classified as a differential equation. However, I'm curious if there is a more specific name for something like this...

Thanks!

 

[PeroK]

The brief answer is that your view of differential equations is too narrow. For example, the simplest DE is:

$\frac{dy}{dt} = f(t)$

Your equation appears to be of this form.

 

[HallsofIvy]

Just as you can have "systems of equations" of numbers, so you can have systems of differential equations.

For example, you can have a system of equations of the form $\frac{dx}{dt}= 3\frac{dy}{dt}+ 3x- 2y$ and $\frac{dy}{dt}= 3x- 4y$.