We're now ready to solve non homogeneous second order

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

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

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

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

Homogeneous differential equation.

A homogeneous solution.

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.

And now, like I just showed you before I cleared the screen, our general solution of this non homogeneous equation is going to be our particular solution plus the general solution to the homogeneous equation.

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 said j is a particular solution for the non homogeneous equation, or that this expression is equal to g of x.

In the next video I'll actually do a non homogeneous equation, and show you that the Laplace Transform applies equally well there.

Construction materials, especially cement, are homogeneous products.

So this is what makes it homogeneous.

What does a homogeneous differential equation mean?

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

Well, this is this the homogeneous, right?

So yes, this is a homogeneous equation.

There should be some shorthand notation for homogeneous.

You get the general solution of the homogeneous.

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.

Schwannomas are homogeneous tumors, consisting only of Schwann cells.

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

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

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

Processing a homogeneous or heterogeneous mix to get pure matter.

look out at the ocean and see this homogeneous sea.

And then you could add the homogeneous solution to that.

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

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

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

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

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.

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.

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

Because I think you know how to solve the essentially, the homogeneous version.