Homogeneous differential equation.

Let's do some more nonhomogeneous equations.

Nigerian Institute of Homeopathy

So we solved the homogeneous equation.

What does a homogeneous differential equation mean?

That this is a solution to our inhomogeneous equation, and that any solution to our inhomogeneous equation takes this form right here.

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 the inhomogeneous equation looks like this.

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

You essentially solve the homogeneous equation.

Schwannomas are homogeneous tumors, consisting only of Schwann cells.

And if we look at our original problem, the general solution out of this nonhomogeneous equation would be this which is the general solution to the homogeneous equation, which we've done many videos on plus now our particular solution that we solved using the method of undetermined coefficient.

But what about the case when you're solving the inhomogeneous equation.

Now, we just said that any solution to an inhomogeneous

You get the general solution of the homogeneous.

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

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

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

And that's all and good, but in order to get the general solution of this nonhomogeneous equation, I have to take the solution of the nonhomogeneous equation, if this were equal to 0, and then add that to a particular solution that satisfies this equation.

But even this monolithic system of control is porous.

That is going to be equal to b and that this is going to be equal to the 0 vector because this is a solution to our homogeneous equation.

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

We said that h is a solution for the homogeneous equation, or that this expression is equal to 0.

So anyway, let's take these and substitute them back into this nonhomogeneous equation.

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

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

I had a vision of 10 girls sitting in a cabin cozily reading books in their matching nightgowns.

Economies of scale tend to favour uniform approaches in large scale centralised schemes for the restoration of degraded lands.

And that's really what you're doing it the method of undetermined coefficients.

Don't put it all in the brain, but put some of the control in tuned feet, legs and even body.

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

Now why am I so concerned with this, and I've been kind of fixated on this inhomogeneous equation for some time.

Far from it. The same disproportionate patterns of school assignment exist throughout much of Central and Eastern Europe.

These tuned structures allow the spines, friction pads and ultimately the adhesive hairs to grab onto very challenging, difficult surfaces.

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.

We are convinced that the proposed diversification fund is an invitation to invest in the harmonious development of our continent and, by extension, in peace.

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

This calls for a kind of liberalism that is now lacking in Russia, one that stands for freedom, reform, and the nation state.

This is social solidarity that evolves along lines of kinship and religion, underpinned by a sense of belonging to the same homogenous group.

And we said in the last video that you can kind of given this you can kind of think of the solution set to the inhomogeneous equation is equivalent to some particular solution, let's call that x particular, some particular solution, plus some member of your null space.

And now in the last example, the nonhomogeneous part was 3e to the 2x.

It is no accident, for example, that Europe s most successful welfare states were created in ethnically homogeneous Scandinavia.

Then and now, Vietnam was the locus of a struggle between the vision of a monolithic Asia and that of an Asia that is open internally and to the world.

Such differences can be more significant than the differences between groups, especially in the case of heterogeneous populations and value systems.

. As sanctions are being lifted, South Africa has come under increasing international pressure to discontinue its unwieldy and sometimes inconsistent trade policies.