When I learned differential calculus, my instructor spoke only in terms of x's & y's. I could differentiate, but had absolutely no idea what I was doing or how it applied. My mentor pulled me aside, gave me a function, f(x)=x^2, & made note that the function was modeling a vehicle's position in space over time. He then asked me what the vehicle's velocity was at some time, t. f'(x)=2x. In other words, the vehicle was accelerating at a rate of 2mph per hour. Okay, now I get it. I see how it applies. I get why we use it. He did the same thing for integrals. My mentor is no longer around & now I am back in the same position - I am solving differential equations but have absolutely no idea what I'm doing. Can we use the vehicle's position over time scenario? A diff eq involves a function & it's derivative, right? So, x^2 + 2x = ? I'm not even sure if I understand that operation -why in the world would you add a function & it's derivative in the first place? What should we include on the other side of the equation & what would that mean?