2. Consider the equation: dy = y² + 2yt +t² - 2y – 2t – 1 dt a. Find a change of variable that transforms the equation into an autonomous equation change of variable: new equation: b. Sketch the phase line for the resulting equation and use it to sketch graphs of the long-term behaviors of all the qualitatively different solutions for the new variable, and then for the original equation.
2. Consider the equation: dy = y² + 2yt +t² - 2y – 2t – 1 dt a. Find a change of variable that transforms the equation into an autonomous equation change of variable: new equation: b. Sketch the phase line for the resulting equation and use it to sketch graphs of the long-term behaviors of all the qualitatively different solutions for the new variable, and then for the original equation.
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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![2. Consider the equation:
dy
y2 + 2yt + t2 – 2y – 2t – 1
dt
a. Find a change of variable that transforms the equation into an autonomous equation
change of variable:
new equation:
b. Sketch the phase line for the resulting equation and use it to sketch graphs of the long-term
behaviors of all the qualitatively different solutions for the new variable, and then for the original
equation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa86b2d75-dc89-44ee-816d-e64b811f53cb%2F4e1d3315-7d36-491c-be83-373a720c9ad3%2Famro1m9_processed.png&w=3840&q=75)
Transcribed Image Text:2. Consider the equation:
dy
y2 + 2yt + t2 – 2y – 2t – 1
dt
a. Find a change of variable that transforms the equation into an autonomous equation
change of variable:
new equation:
b. Sketch the phase line for the resulting equation and use it to sketch graphs of the long-term
behaviors of all the qualitatively different solutions for the new variable, and then for the original
equation.
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