13. r' = x² + x + 1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Was needing some help on #13 and the proper way to create the phase line diagram. Does x=-1 and x=-2 seem correct?

Equilibrium solutions and phase lines. Find the equilibrium solutions for
each of the differential equations in Exercise Group 1.3.8.8-13. Draw the phase
line for each equation and classify each equilibrium solution as a sink, a source,
or a node.
8. y' = 2y-5
10.
dx
dt
=
= (x² - 1)(x - 2)
12. T' (x² + 1)(x - 1)
9.
11.
d.x
dt
=
dy
dr
(x - 1)(x+2)
=
sin 2y
13. x' = x²+x+1
Transcribed Image Text:Equilibrium solutions and phase lines. Find the equilibrium solutions for each of the differential equations in Exercise Group 1.3.8.8-13. Draw the phase line for each equation and classify each equilibrium solution as a sink, a source, or a node. 8. y' = 2y-5 10. dx dt = = (x² - 1)(x - 2) 12. T' (x² + 1)(x - 1) 9. 11. d.x dt = dy dr (x - 1)(x+2) = sin 2y 13. x' = x²+x+1
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