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Sketch a direction field for the differential equation. Then use it to sketch three solution curves.$ y' = 1 + y $

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Calculus 2 / BC

Chapter 9

Differential Equations

Section 2

Direction Fields and Euler's Method

Baylor University

University of Nottingham

Boston College

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.

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Sketch a direction field f…

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Sketch the direction field…

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$9-10$ Sketch a direction …

actual equation. We were asked to use this occasion. Grab the slope feel solutions. The creation were given one before the draft. But a slip of you so particular take Why to be some constant c Every young numbers X Any remember half that well of wine going to be 1/2. Why one? In other words, say it's easy. Why zero at every point along in particular value. See slow any Why it c zero going to you zero So we have wars on a one. Hey you! Why is it 0.5? Have a all right by 11 Why is it 2.5? Have a good one is very Why is it warm? What? Why is it one from five quarters? Have a look off one. Do you see this? Increases is broken extending from the way already today. Wrong It is anything away from the organ? Likewise. Why is negative? No one had a stroke of May 25. Get this is very rough. Both feel bad around here. I think the general idea Foreign three solutions. It's different initial values. For example, let's take initial value. Why is your people zero? They don't have a point goalless and like, are you? We'll see if this is simply the bars on one. It's just the horizontal one, Mother. Initial condition. Why you one I'll draw this red. You're one. And you worked too. Graphic. Simply follow you See that? This is a That's access, baby, isn't there? Looks a little bit right now. One more initial value will take a negative one. Now we've got one for below. And on the and apparatus Marine, we have a 0.0 native one. You said his expert. His name. It's a purchase. The absolute Y zero. Mr Perfect is that purchase. This is another kind of experiential ocean support and reflected across the X axis.

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