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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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Question

Solve letter (b) for iii y'=y^3+y

**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 \( y' = f(x)g(y) \). i. \( y' = \sin(x) \cos(y) \) ii. \( y' = \sin(y)e^y \) iii. \( y' = y^3 + y \) iv. \( y' = y(4 - y)(y - 3)(y - 10) \) --- **(b)** For each differential equation, list all equilibrium solutions and classify each as stable, unstable, or semistable. i. \( y' = y^3 - y \) ii. \( y' = \sin(y) e^y \) iii. \( y' = x(x - 1)(y - 2)(x - 3)(y - 4) \) iv. \( y' = y^3 + y \) v. \( y' = x^2 y^2 + 2x^2 y + x^2 \)
Transcribed Image Text:**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 \( y' = f(x)g(y) \). i. \( y' = \sin(x) \cos(y) \) ii. \( y' = \sin(y)e^y \) iii. \( y' = y^3 + y \) iv. \( y' = y(4 - y)(y - 3)(y - 10) \) --- **(b)** For each differential equation, list all equilibrium solutions and classify each as stable, unstable, or semistable. i. \( y' = y^3 - y \) ii. \( y' = \sin(y) e^y \) iii. \( y' = x(x - 1)(y - 2)(x - 3)(y - 4) \) iv. \( y' = y^3 + y \) v. \( y' = x^2 y^2 + 2x^2 y + x^2 \)
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