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Sketch the direction field of the differential equation. Then use it to sketch a solution curve that passes through the given point.$ y' = y - 2x, (1,0) $

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Calculus 2 / BC

Chapter 9

Differential Equations

Section 2

Direction Fields and Euler's Method

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Lectures

13:37

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. An ordinary differential equation (ODE) is a differential equation containing one or more derivatives of a function and their rates of change with respect to the function itself; it can be used to model a wide variety of phenomena. Differential equations can be used to describe many phenomena in physics, including sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, quantum mechanics, and general relativity.

33:32

03:19

Sketch the direction field…

0:00

13:30

00:24

00:27

02:58

11:23

you're giving. Get until equation. And that one plane we were asked to find a field of this equation. Our differential equation is why find one and the plane is one drop slope. Deal. Withdraw for the plane and I'll make measurements on the X and Y axis if we set the slope. Why? Prime City Seeing real numbers follows this Z Y minus two. Therefore, wine what to X plus e line. But look, too. It has mine except zero C and points on the line. You have that? Why climate that point is going to be so secret. You know, find all the point had why I find that point before zero use all the points that lie in the line. Wife A particular This includes Oregon the point one, you and they want to for reforms in between the lines plus one that would find another point. But with white kind of that one. And you know the point. Buying a line white to explore. This includes the 0.1 Have a smoke one Here we go up. Warned him in over one. Well, the trick why? We also have excellent of X here and all the other points in this line had the same spoke si is equal to positive too Being a slope of tin These other points line line white the way what to so in particular you're to live in this line. It's that slow to you go for over one little hard to see Yeah, it looks a little steeper. We also have an exit Except those X equals negative one began Global Super The line, of course. Did it point line it have the same slope so we could see it. As you get further and further away from the line. Why was plus one? The slopes are going to get steeper and steeper. Do something with this Now C is for you. Less than zero. See that again? Have you parallel lines? It looked too. You go further and further away from the line. White one from flying. That won't do more and more. Maybe. Look, something like that Oxidation of the actually looked. Did you hear? What? Kurt? So we have representation of us here and we're asking fine solution which has a 0.10 So I'm going to read. Massey has a 0.10 Will look with this on a graph 10 and we'll follow the blue wine segments. Yes, it's possible. Quickly is X. There's two problems. This goes for you. See, that's extra. I want a little bit. Message the line. Why you two x one. Level out client again as we follow that line is NASA to

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