Use the differential equation below to answer the following questions: y = ¼ y²³ – 4y 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 = 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 ∞. • Enter NONE if the solution curves do not display that behavior on any interval. ● ● a. Increasing: b. Decreasing: c. Concave Up: d. Concave Down: PART 3. Determine the long-term behavior for the solution corresponding to each initial condition: a. y(0) = 22 | Choose one b. y(0) = 18 Choose one c. y(0) = -2 Choose one () <>
Use the differential equation below to answer the following questions: y = ¼ y²³ – 4y 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 = 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 ∞. • Enter NONE if the solution curves do not display that behavior on any interval. ● ● a. Increasing: b. Decreasing: c. Concave Up: d. Concave Down: PART 3. Determine the long-term behavior for the solution corresponding to each initial condition: a. y(0) = 22 | Choose one b. y(0) = 18 Choose one c. y(0) = -2 Choose one () <>
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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Transcribed Image Text:Use the differential equation below to answer the following questions:
y² = y² - 4y
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:
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:
b. Decreasing:
c. Concave Up:
d. Concave Down:
PART 3. Determine the long-term behavior for the solution corresponding to each
initial condition:
a. y(0) = 22
b. y(0) = 18
c. y(0) = -2
Choose one
Choose one
Choose one
î
<>
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