Question

differential equations....yes that's fine but what does it mean? The book tries to get me to understand the equation by pointing at another equation...and then waving their hands at it like that is an explanation: So dy/dx = x^3 + 2x^2 - x
what does it really mean?

Answer 1

the changes in y --when x changes are this wave form and I graph the equation...

but to solve the diff eq multiply both sides by dx which becomes: the changes in y are equal to x^3 + 2x^2 - x changes in x?

but what does this tell me about anything? anybody?

Answer 2

are you asking how are DEs useful in real life?

Answer 3

not really (maybe)??! I'm more wondering how this helps me interpret what the equation is describing.

Answer 4

A differential equation describes the rate of change of something. dy/dx tells you how much y changes, for a tiny change in x.

"but to solve the diff eq multiply both sides by dx which becomes: the changes in y are equal to x^3 + 2x^2 - x changes in x?"

That's when you're finding the original function. dy/dx only tells you the rate of change of the original function.

Answer 5

eg speed is a rate of change (rate of change of distance over time). An object moving at 60m/s tells you that for each second that passes (change in time), the object moves 60m (change in distance).

Answer 6

right so in physics y = position; y'=velocity; y''=acceleration --- so figuring that out with diff eq seems like the harder way to figure things out. If you know acceleration and you want to know position you integrate(antiderivitive twice)...

Answer 7

" so figuring that out with diff eq seems like the harder way to figure things out." it isn't very difficult if it's a simple equation.