their direction field in the (t, y)-plane. Moreover, on each direction field, draw two solu- tions that satisfy y(1) = 3 and y(1) = 1 respectively. (a) y' (t) = y/2-1, (b) y' (t) = −y/2+1 (a) Which of the previous two differential equations in Problem 1 has unstable (divergent) solutions? Solve it, and show the expressions of two curves that you draw in the divergent direction field.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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I have attached the two equations

their direction field in the (t, y)-plane. Moreover, on each direction field, draw two solu-
tions that satisfy y(1) = 3 and y(1) = 1 respectively.
(a) y' (t) = y/2-1,
(b) y' (t) = −y/2+1
Transcribed Image Text:their direction field in the (t, y)-plane. Moreover, on each direction field, draw two solu- tions that satisfy y(1) = 3 and y(1) = 1 respectively. (a) y' (t) = y/2-1, (b) y' (t) = −y/2+1
(a) Which of the previous two differential equations in Problem 1 has unstable (divergent)
solutions? Solve it, and show the expressions of two curves that you draw in the divergent
direction field.
Transcribed Image Text:(a) Which of the previous two differential equations in Problem 1 has unstable (divergent) solutions? Solve it, and show the expressions of two curves that you draw in the divergent direction field.
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