Answered: 3. Eight systems of differential…

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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Eight systems of differential equations and four direction fields are given below. Determine the system that corresponds to each direction field. You should do this without using technology.

3. Eight systems of differential equations and four direction fields are given below. Determine the
system that corresponds to each direction field. You should do this without using technology.
dx
dy
= -x,
= y - 1
dt
dt
dx
II
dy
= * - 1,
dr
= y
dx
III
= x+ 2y.
dy
=-y
dt
dy
= 2x,
= y
dt
dx
dy
= x,
= 2y
dt
dt
dx
dy
= -y
VI
= x- 1,
dt
dy
= -y
= x- 2y,
dt
dy
=-y
dr
(a)
(b)
(e)
(d)
11111*
II

Expert Solution

Step 1

Further when and are both positive is decreasing and when both and are negative it is increasing. This is not possible for case(iii). It only matches with (viii). Therefore the direction field in (b) matches with case (viii)

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