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Use the differential equation below to answer the following questions: y = y² – 7y + 6 PART 1. Find the constant solutions of this differential equation. • If there is more than one, enter the y-values as a comma separated list (e.g. 3,4). Enter NONE if there are no constant solutions. ● a. Constant Solution(s): y = 1,6 PART 2. Find the open interval(s) for y on which the solution curves are increasing / decreasing / concave up / concave down. Type your answers using interval notation. • If necessary, use a capital U to denote union Use -INF and INF to denote -∞ and co. Enter NONE if the solution curves do not display that behavior on any interval. ● ● a. Increasing: (-∞,1) U (6,∞) b. Decreasing: (1,6) c. Concave Up: d. Concave Down: 717,00) 00₁717) ∞. PART 3. Determine the long-term behavior for the solution corresponding to each initial condition: a. y(0) = 7 increases without bound b. y(0) = 2 asymptotically approaches a constant solution î c. y(0) = 0 asymptotically approaches a constant solution -

Use the differential equation below to answer the following questions: y = y² – 7y + 6 PART 1. Find the constant solutions of this differential equation. • If there is more than one, enter the y-values as a comma separated list (e.g. 3,4). Enter NONE if there are no constant solutions. ● a. Constant Solution(s): y = 1,6 PART 2. Find the open interval(s) for y on which the solution curves are increasing / decreasing / concave up / concave down. Type your answers using interval notation. • If necessary, use a capital U to denote union Use -INF and INF to denote -∞ and co. Enter NONE if the solution curves do not display that behavior on any interval. ● ● a. Increasing: (-∞,1) U (6,∞) b. Decreasing: (1,6) c. Concave Up: d. Concave Down: 717,00) 00₁717) ∞. PART 3. Determine the long-term behavior for the solution corresponding to each initial condition: a. y(0) = 7 increases without bound b. y(0) = 2 asymptotically approaches a constant solution î c. y(0) = 0 asymptotically approaches a constant solution -

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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Use the differential equation below to answer the following questions: y = y² − 7y + 6 PART 1. Find the constant solutions of this differential equation. • If there is more than one, enter the y-values as a comma separated list (e.g. 3,4). Enter NONE if there are no constant solutions. a. Constant Solution (s): y = 1,6 PART 2. Find the open interval(s) for y on which the solution curves are increasing / decreasing /concave up /concave down. Type your answers using interval notation. • If necessary, use a capital U to denote union Use -INF and INF to denote - and ∞o. Enter NONE if the solution curves do not display that behavior on any interval. ● ● ● a. Increasing: (-∞,1) U (6,∞ ) b. Decreasing: (1,6) c. Concave Up: (1717,00) d. Concave Down: 7|2 PART 3. Determine the long-term behavior for the solution corresponding to each initial condition: a. y(0) = 7 increases without bound b. y(0) = 2 c. y(0) = 0 asymptotically approaches a constant solution asymptotically approaches a constant solution î
Transcribed Image Text:Use the differential equation below to answer the following questions: y = y² − 7y + 6 PART 1. Find the constant solutions of this differential equation. • If there is more than one, enter the y-values as a comma separated list (e.g. 3,4). Enter NONE if there are no constant solutions. a. Constant Solution (s): y = 1,6 PART 2. Find the open interval(s) for y on which the solution curves are increasing / decreasing /concave up /concave down. Type your answers using interval notation. • If necessary, use a capital U to denote union Use -INF and INF to denote - and ∞o. Enter NONE if the solution curves do not display that behavior on any interval. ● ● ● a. Increasing: (-∞,1) U (6,∞ ) b. Decreasing: (1,6) c. Concave Up: (1717,00) d. Concave Down: 7|2 PART 3. Determine the long-term behavior for the solution corresponding to each initial condition: a. y(0) = 7 increases without bound b. y(0) = 2 c. y(0) = 0 asymptotically approaches a constant solution asymptotically approaches a constant solution î
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