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4. Construct a slope field for the differential equation dy = (t + 1)(y – 1) dt

4. Construct a slope field for the differential equation dy = (t + 1)(y – 1) dt

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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Differential equation

Please write your explanation and don't use the calculator.

Construct a slope field for the differential equation
??
?? = (? + 1)(? − 1)
for −2 < ? < 2 and −2 < ? < 2, and use your slope field to sketch the solution that satisfies the initial 
condition ?(0) = 0. (Draw something like 25 minitangents to cover the given square, being sure to 
show enough to see all the qualitatively different behaviors of the slope field, and enough to show the 
behavior of the solution.) (Be sure to show your work for how you get the mini-tangents—don’t just 
draw the field.)

4. Construct a slope field for the differential equation dy = (t + 1)(y – 1) %3D dt for –2 < t < 2 and -2 < y < 2, and use your slope field to sketch the solution that satisfies the initial condition y(0) = 0. (Draw something like 25 minitangents to cover the given square, being sure to show enough to see all the qualitatively different behaviors of the slope field, and enough to show the behavior of the solution.) (Be sure to show your work for how you get the mini-tangents-don't just draw the field.)
Transcribed Image Text:4. Construct a slope field for the differential equation dy = (t + 1)(y – 1) %3D dt for –2 < t < 2 and -2 < y < 2, and use your slope field to sketch the solution that satisfies the initial condition y(0) = 0. (Draw something like 25 minitangents to cover the given square, being sure to show enough to see all the qualitatively different behaviors of the slope field, and enough to show the behavior of the solution.) (Be sure to show your work for how you get the mini-tangents-don't just draw the field.)
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