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Suppose that = p(y) is an autonomous equation satisfying all four of the following dt conditions: (i) The only equilibrium solutions are y = -3 and y = 5 (ii) P(y) < 0 for y < -3 (iii) p(y) > 0 for -3 < y < 5 (iv) p(y) > 0 for y > 5 Let y(t) be a solution such that y(0) = -4. If it exists, determine lim y(t). O -4 O 5 O This limit does not exist.

Suppose that = p(y) is an autonomous equation satisfying all four of the following dt conditions: (i) The only equilibrium solutions are y = -3 and y = 5 (ii) P(y) < 0 for y < -3 (iii) p(y) > 0 for -3 < y < 5 (iv) p(y) > 0 for y > 5 Let y(t) be a solution such that y(0) = -4. If it exists, determine lim y(t). O -4 O 5 O This limit does not exist.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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dy = p(y) is an autonomous equation satisfying all four of the following dt Suppose that conditions: -3 and y = 5 (i) The only equilibrium solutions are y (ii) p(y) < 0 for y < -3 (iii) p(y) > 0 for -3 < y < 5 (iv) p(y) > 0 for y > 5 | Let y(t) be a solution such that y(0) = -4. If it exists, determine lim y(t). t→∞ -3 -4 This limit does not exist.
Transcribed Image Text:dy = p(y) is an autonomous equation satisfying all four of the following dt Suppose that conditions: -3 and y = 5 (i) The only equilibrium solutions are y (ii) p(y) < 0 for y < -3 (iii) p(y) > 0 for -3 < y < 5 (iv) p(y) > 0 for y > 5 | Let y(t) be a solution such that y(0) = -4. If it exists, determine lim y(t). t→∞ -3 -4 This limit does not exist.
Expert Solution
Step 1

Given that dydt=p(y) that satisfies the given condition. 

i.e. py=y+3y-52

     dydt=y+3y-52

    dyy+3y-5)2=dt

i.e. Ay+3+By-5+Cy-52dy = dt                               (1)

where 1y+3y-52=Ay+3+By-5+Cy-52

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