Examples of using Differential equations in English and their translations into Thai
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So the differential equations.
That's true with regular equations or differential equations.
Differential equations are something different.
Least the solvable differential equations.
This differential equations problem was literally just a problem in using the quadratic equation. .
We know the three particular solutions to the following differential equations.
And if you're taking differential equations, it might be on an exam.
That's what this playlist will deal with, ordinary differential equations.
A lot of what you will learn in differential equations is really just different bags of tricks.
And actually, we're going to start solving non-homogeneous differential equations.
Now within ordinary differential equations, there's two ways of classifying, and they kind of overlap.
So second order linear homogeneous-- because they equal 0-- differential equations.
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 when you study exact equations in differential equations, you will see this a lot more.
There isn't just one tool or one theory that will solve all differential equations.
That makes sense, because the separable differential equations are really just implicit derivatives backwards.
And I think you will see that these, in some ways, are the most fun differential equations to solve.
And that's a fairly useful thing, because differential equations is something that shows up in a whole set of different fields.
And I'm getting these problems from page 80 of my old college differential equations books.
We will now move from the world of first order differential equations to the world of second order differential equations.
I'm just trying to show you as many examples as possible of solving exact differential equations.
And I'm getting this from my college differential equations book. x squared times the second derivative of y with respect to x, plus x times the first derivative of y with respect to x, plus 2y is equal to sine of x.
Welcome to this first video, and actually the first video in the playlist on differential equations.
Because later on when you want to know more theory of differential equations-- and that's really the whole point about learning this if your whole goal isn't just to pass an exam-- it's good to know.
Now before we go on, in the next one I will show you some fairly straightforward differential equations to solve.
Let's solve another 2nd order linear homogeneous differential equation.
Because this is a second order differential equation.
And we get a separable second order differential equation.
Homogeneous differential equation.

