A homogeneous solution.

Maybe we'll call this the homogeneous solution. y homogeneous.

What does a homogeneous differential equation mean?

So yes, this is a homogeneous equation.

Homogeneous differential equation.

And that worked out well, because, h for homogeneous. h is solution for homogeneous.

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

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

That the general solution of this non homogeneous equation is actually the general solution of the homogeneous equation plus a particular solution.

This is a homogeneous equation, because we have a 0 there.

Processing a homogeneous or heterogeneous mix to get pure matter.

Egypt, by contrast, is relatively homogeneous.

Homogeneous mix of multiple pure materials

And this one is called homogeneous.

So we solved the homogeneous equation.

You essentially solve the homogeneous equation.

We could say that it is equal to a homogeneous solution.

Construction materials, especially cement, are homogeneous products.

So this is what makes it homogeneous.

And we'll talk about why it's homogeneous.

Well, this is this the homogeneous, right?

Fortunately for the US, the Taliban is no longer a homogeneous group.

It can be a homogeneous product, especially at the producer processor level.

So let's say that h is a solution of the homogeneous equation.

There should be some shorthand notation for homogeneous.

You get the general solution of the homogeneous.

This requires the continued development of a homogeneous data record from multiple instruments.

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

Schwannomas are homogeneous tumors, consisting only of Schwann cells.

We're now ready to solve non homogeneous second order

So you could say it's plus some homogeneous solution.

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

Ethnicity The population of the county is almost homogeneous, with a Hungarian majority (94.1 ).

The Nubians constituted a homogeneous group within Egyptian society, speaking Arabic with their own dialect.

look out at the ocean and see this homogeneous sea.

And then you could add the homogeneous solution to that.

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

Is that particular solution, plus some homogeneous solution, a solution to Ax is equal to b?

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

And that it's the general solution for this non homogeneous equation.

Plus some homogeneous solution, so some member of the null space.

And actually, we're going to start solving non homogeneous differential equations.

Korea is chiefly populated by a highly homogeneous ethnic group, the Koreans, who speak the Korean language.

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