So that's separable.

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.

A differential is a really, really, really, really infinitely small difference.

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

I just took the antiderivative of both sides.

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

Equation

Equation

So how do you think about this graphically?

That means that at some point, it'll have to turn around and fall back upon itself. So let's just subtract those two equations.

And this one is called homogeneous.

But anyway, there we have it.

We could call that c1 or something.

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

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

Polar Equation

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Where's the equation?

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

Exact 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.

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So, I'll see you in the part 2 of using the quadratic equation.

But anyway I don't want to get caught up in terminology.

Let me write that down.

So I'll just re write that as c.

Is it possible to represent this function as a Gaussian?

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

One, trying to figure out whether the equations are exact.

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.

But what we've said, I know you might have lost track we did all this math is we said, this equation minus 9x squared minus 9x plus 6.

Is ( 1, 7) is solution for the equations below.

Which is equal to a squared.

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It would open downward and it would go down twice as fast.