Differentiating results in us knowing how large y-output changes compared to qan amount of x-input in the function f(x)=y.
Integrating is, uh, just “the summation” of all y-outputs as a result of x-inputs.
Now, what does a DE tell me? And what does solving it do?
In: Mathematics
It’s been a loooong time since I did differential equations and I’m sure I won’t be able to solve anything if you ask me now (without reviewing) but here’s my 5 cents.
You already knkw about derivatives. As other comments have already said, a differential equation is an equation that has one or more derivatives in it. You already know about integrals – integrals are actually the way to solving differential equations. The simplest integral you can find ( integral(1″dx) = x + C ) is actually the solution for the differential equation dy/dx = 1.
So in the most basic of ways, what a differential equation at its simplest is really just the same as a derivative. It shows you the rate of change of something with respect to another thing.
Now how about those with 2nd derivatives and more complex stuff you see when you start at the differential equations course your engineering school offers you? Turns out the world is not so simple that you can solve for all those things using just your simple derivatives and integrals. For more complicated events you need to use more complicated equations and more complicated solutions. The number of derivatives in each equation may change and there might be more clutter in them, but in essence what they wanna show you is the same – how something changes with respect to another thing. And solving those equations will tell you how much of that one thing is there when there’s this much of that another thing.
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