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Use a computer algebra system to draw a direction field for the differential equation $ y' = y^3 - 4y. $ Get a printout and sketch on it solutions that satisfy the initial condition $ y(0) = c $ for various of $ c. $ For what values of $ c $ does $ \lim $ $_{t \to\infty} y(t) $ exist? What are the possible values for this limit?

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$L=\lim _{t \rightarrow \infty} y(t)$ exists for $-2 \leq c \leq 2$$L=\pm 2$ for $0=\pm 2$ and $L=0$ for $-2<0<2$

Calculus 2 / BC

Chapter 9

Differential Equations

Section 2

Direction Fields and Euler's Method

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

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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Use a computer algebra sys…

03:23

(a) Draw a direction field…

01:47

draw a direction field for…

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03:39

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