Differential equations. Autonomous systems and stability Show that for: x´=ax+by y´=cx+dy Where ad-cd=0, it falls into the following types: a) Every point is an equilibrium point. b) There is a line of equilibrium points, each trajectory is a straight line that approaches an equilibrium point. c)There is a line of equilibrium points, and each orbit a line parallel to the line of equilibrium points.
Differential equations. Autonomous systems and stability Show that for: x´=ax+by y´=cx+dy Where ad-cd=0, it falls into the following types: a) Every point is an equilibrium point. b) There is a line of equilibrium points, each trajectory is a straight line that approaches an equilibrium point. c)There is a line of equilibrium points, and each orbit a line parallel to the line of equilibrium points.
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 equations. Autonomous systems and stability
Show that for:
x´=ax+by
y´=cx+dy
Where ad-cd=0, it falls into the following types:
a) Every point is an equilibrium point.
b) There is a line of equilibrium points, each trajectory is a straight line that approaches an equilibrium point.
c)There is a line of equilibrium points, and each orbit a line parallel to the line of equilibrium points.
Please be as clear as possible. Show and explain all the steps in detail. Use definitions if necessary. Thank you very much.
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