1. If the general solution for a system of differential equations of the form dx ax + by сх + dy %3D dt is -2t + k2e-t what do solutions in phase plane look like? What do solutions that are not straight lines look like? Do they curve a particular way? Figure out a way to use the general solution (without technology) to decide. Explain and graph your ideas.

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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1. If the general solution for a system of differential equations of the form
dx
ax + by
%3D
dy
dt
cx + dy
r(t)
() = kie-2t ()
2
+ k2e-
1
4
what do solutions in phase plane look like? What do solutions that are not straight lines look like?
Do they curve a particular way? Figure out a way to use the general solution (without technology)
to decide. Explain and graph your ideas.
2. Repeat problem 1 for the general solution
(8) = khe (
x(t)
y(t)
+ kze3t
3. Repeat problem 1 for the general solution
()
= kje" C)
+ kze-2t
-3
2
is
Transcribed Image Text:1. If the general solution for a system of differential equations of the form dx ax + by %3D dy dt cx + dy r(t) () = kie-2t () 2 + k2e- 1 4 what do solutions in phase plane look like? What do solutions that are not straight lines look like? Do they curve a particular way? Figure out a way to use the general solution (without technology) to decide. Explain and graph your ideas. 2. Repeat problem 1 for the general solution (8) = khe ( x(t) y(t) + kze3t 3. Repeat problem 1 for the general solution () = kje" C) + kze-2t -3 2 is
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