I think we've got him pegged.

That's what this playlist will deal with, ordinary differential equations.

So there's two big classifications.

Homogeneous differential equation.

So we'll just assume that that is our psi.

They say that y of 0 is equal to negative 1.

Or if you wanted to write it out, psi is this thing.

I just took the antiderivative of both sides.

And this one is called homogeneous.

But anyway, there we have it.

We could call that c1 or something.

So it's first order.

What does a homogeneous differential equation mean?

And then you could solve for c.

But anyway, that's just a little technicality.

And it might seem really fancy.

So they say y1 of x is equal to e to the minus 3x.

I would say a lot easier than what we did in the previous first order homogeneous difference equations, or the exact equations.

Now before we go on, in the next one I'll show you some fairly straightforward differential equations to solve.

So I'll just re write that as c.

Let's do one more homogeneous differential equation, or first order homogeneous differential equation, to differentiate it from the homogeneous linear differential equations we'll do later.

11 45.

Differentiation

That makes sense, because the separable differential equations are really just implicit derivatives backwards.

So what is a differential equation?

And then you go forward for all of time.

Divided by 2xy.

So the differential equations.

So this example I just wrote here, this is a second order

And there you have it.

But anyway, I've run out of time, and hopefully that gives you a good at least survey of what a differential equation is.

And this is actually a separable differential equation in and of itself.

We're going to start embarking on higher order differential equations.

Though I joke about it,

And this implicitly defined function, or curve, or however you want to call it, is the solution to our original homogeneous first order differential equation.

Now I introduce you to the concept of exact equations.

The color picking's the hard part.

You know what an equation is.

So let's say that I'm just writing now.

Well, 1 plus 2 minus 3, well that equals 0 again.

You've seen it in physics, where you said, oh, it's something that has a magnitude and a direction.

I think I'll eventually do a play list on essentially an introductory course on differential equations that you would take at college.

I will now introduce you to the idea of a homogeneous differential equation.

And even within differential equations, we'll learn later there's a different type of homogeneous differential equation.

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