Ice nucleation for Weather Modification .

Homogeneous differential equation.

So in all of these homogeneous equations and obviously, we don't know it's homogeneous yet.

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.

Homogeneous mix of multiple pure materials

And this one is called homogeneous.

So this is what makes it homogeneous.

What does a homogeneous differential equation mean?

So yes, this is a homogeneous equation.

Conformity is an essential element of our homogeneous community.

Conformity is an essential element of our homogeneous community.

Let's solve another 2nd order linear homogeneous differential equation.

Processing a homogeneous or heterogeneous mix to get pure matter.

look out at the ocean and see this homogeneous sea.

What we learn is that if it can be homogeneous, if this is a homogeneous differential equation, that we can make a variable substitution.

So second order linear homogeneous because they equal 0 differential equations.

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

But anyway, for this purpose, I'm going to show you homogeneous differential equations.

Those are called homogeneous linear differential equations, but they mean something actually quite different.

But anyway, these are useful properties to maybe internalize for second order homogeneous linear differential equations.

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

So the reason why this one is called homogeneous is because you have it equal to 0.

So if you had no outside force, if this was zero you'd have a homogeneous differential equation.

And by setting this equal to 0, I have now introduced you to the other form of homogeneous differential equation.

But before I need to show you that, I need to tell you, what does it mean to be homogeneous?

Through chemical composition and physical attributes, homogeneous portion of matter that separated from its environment in its expansion through a surface.

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

So they're not Perfectly symmetric and homogeneous and so on but by and large they can be and so our approximations are not bad.

For one thing, it's unified, has a relatively homogeneous population, one language, a huge internal market and rich resources, a favorable climate and much more.

We solved that seemingly inseparable differential equation by recognizing that it was homogeneous, and making that variable substitution v is equal to y over x.

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.

But now this F, all of a sudden, it's kind of a non homogeneous term, it's what the outside force you're applying to this mass.

And actually, these are more useful, and in some ways, easier to do than the homogeneous and the exact equations that we've been doing so far.

The aluminum oxide nanoparticles, which are microscopically fine and uniform in size, attract the humidity and the moisture in the air, and they can it basically forms like a nucleation process, where the moisture condenses on these particles.

Homogeneous is the same word that we use for milk, when we say that the milk has been that all the fat clumps have been spread out.

What that means is every time you see this prefix homologous or if you see like Homo sapiens or even the word homosexual or homogeneous, it means same, right?

I've spoken a lot about second order linear homogeneous differential equations in abstract terms, and how if g is a solution, then some constant times g is also a solution.

Or another way to view it is that if g is a solution to this second order linear homogeneous differential equation, then some constant times g is also a solution.

And I haven't made the connection yet on how these second order differential equations are related to the first order ones that I just introduced to these other homogeneous differential equations I introduced you to.

So if g is a solution of the differential equation of this second order linear homogeneous differential equation and h is also a solution, then if you were to add them together, the sum of them is also a solution.

It's exactly equivalent to taking one 325 milligram aspirin tablet, throwing it into the middle of Lake Tahoe, and then stirring it up, obviously with a very big stick, and waiting two years or so until the solution is homogeneous.

And actually, I do see more of a connection between this type of equation and milk where all the fat is spread out, because if you think about it, the solution for all homogeneous equations, when you kind of solve the equation, they always equal 0.

In general, if I have an ideal gas in a container, the pressure exerted on the gas on the side of the container, or actually even at any point within the gas, because it will all become homogeneous at some point and we'll talk about entropy in future videos but the pressure in the container and on its surface, times the volume of the container, is equal to some constant.