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

So there's two big classifications.

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

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.

Well actually, there's a first big one, ordinary and partial differential equations.

And this one is called homogeneous.

But anyway, there we have it.

We could call that c1 or something.

And so, given that it was exact, we knew that a psi would exist where the derivative of psi with respect to x would be equal to this entire expression.

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

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.

So I'll just re write that as c.

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

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.

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.

And let's say we try to do this, and it's not separable, and it's not exact.

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.

And what we're dealing with are going to be first order equations.

But if you look here, you actually could have figured out that this is actually a separable equation.

We're not talking about the Harry Potter end, right at the left side.

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.

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

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

So it's first order.

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

And so c is equal to 7.

And then we unsubstituted it back.

So we get c is equal to 1.