Need explanation of differential equations

Hello, I am a student at the University of Pittsburgh. I am majoring in electrical engineering. I have already successfully completed Calculus 1 and 2. Now I have a class in Differential Equations. I have heard that electrical engineers use differential equations a lot, so you see how important it is that I understand them.

So my situation is this. Yesterday was my first day of Differential Equations class, and as soon as my professor began explaining I knew I was in trouble. To be honest I have no clue what my professor was talking about.

After I got home I tried reading my book and I still don't understand it. Tomorrow is my second class, and I want to figure this out BEFORE I come to it.

Okay so I know what a function is. Example: f(x) = x²+5

This means that you input values of X and get outputs of Y.

I know what a derivative of the above function is. Its a function of the instantaneous rate of change or slope. And the derivative of the above is 2X.

So just what in heck is a differential equation? Can you please explain using the example above if possible? Please use simple examples because if I can understand the key concept I can do more complex stuff.

Its the key concept I'm having trouble understanding.