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=) List the equilibrium solutions of the differential equation y' = (y² - 1) arctan(y)

=) List the equilibrium solutions of the differential equation y' = (y² - 1) arctan(y)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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ATH 12 Worksheet 10: Direction Fields and Euler's Method 1. Differential equations and direction fields Write definitions for the following terms in your own words, then compare with your class- mates: • Differential equation Order of a differential equation • Direction field • Equilibrium solution • Stable equilibrium solution (a) Find the general solution to the differential equation y' = 20e5x + x². (b) Find the particular solution to the initial value problem y' = 6t - 10e²t, y(0) = 11. (c) List the equilibrium solutions of the differential equation y = (y² - 1) arctan(y) A (d) List all equilibrium solutions of the differential equation, and classify the stability of each using a sign chart: y' = y(y - 6)²(y - 10) (e) Use equilibrium solutions and stability analysis (sign chart) to predict the long-term behavior of a system given by the initial value problem P' = P² (P-3) (P-10), P(0) = 8
Transcribed Image Text:ATH 12 Worksheet 10: Direction Fields and Euler's Method 1. Differential equations and direction fields Write definitions for the following terms in your own words, then compare with your class- mates: • Differential equation Order of a differential equation • Direction field • Equilibrium solution • Stable equilibrium solution (a) Find the general solution to the differential equation y' = 20e5x + x². (b) Find the particular solution to the initial value problem y' = 6t - 10e²t, y(0) = 11. (c) List the equilibrium solutions of the differential equation y = (y² - 1) arctan(y) A (d) List all equilibrium solutions of the differential equation, and classify the stability of each using a sign chart: y' = y(y - 6)²(y - 10) (e) Use equilibrium solutions and stability analysis (sign chart) to predict the long-term behavior of a system given by the initial value problem P' = P² (P-3) (P-10), P(0) = 8
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