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(b) For each differential equation, list all equilibrium solutions and classify each as stable, unstable, or semistable. i. ii. y' = y³ − y y' = sin(y)e" iii. iv. y' = y³ + y y' = y(y - 3)³(y - 10)

(b) For each differential equation, list all equilibrium solutions and classify each as stable, unstable, or semistable. i. ii. y' = y³ − y y' = sin(y)e" iii. iv. y' = y³ + y y' = y(y - 3)³(y - 10)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve letter (b) for iii y'=y^3+y

iii. i. ii. i. y' = x(x - 1)(y-2)(x-3)(y-4) y' = sin(y) cos(x) (b) For each differential equation, list all equilibrium solutions and classify each as stable, unstable, or semistable. y' = y³ - y y' = sin(y) ey V. y' = sin(x) cos(y) iii. iv. y = r²y² + 2x²y + x² - Separable differential equations (a) Determine which of the following first order differential equations are separable. For those that are separable, re-write them in a factored form as y' = f(x)g(y). iv. y' = y³ + y y' = y² (y - 3)³(y - 10) y' = ety
Transcribed Image Text:iii. i. ii. i. y' = x(x - 1)(y-2)(x-3)(y-4) y' = sin(y) cos(x) (b) For each differential equation, list all equilibrium solutions and classify each as stable, unstable, or semistable. y' = y³ - y y' = sin(y) ey V. y' = sin(x) cos(y) iii. iv. y = r²y² + 2x²y + x² - Separable differential equations (a) Determine which of the following first order differential equations are separable. For those that are separable, re-write them in a factored form as y' = f(x)g(y). iv. y' = y³ + y y' = y² (y - 3)³(y - 10) y' = ety
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