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CHAPTER 5: Introduction to Systems and Phase
Plane Analysis
EXERCISES 5.2:
Elimination Method for Systems, page 250
1.
Subtracting the second equation in the system from the Frst one, we eliminate
y
and obtain
x
0
+
y
0
=
−
2
y,
y
0
=
x
−
2
y
⇒
x
0
=
−
x.
This equation is separable (also, it is linear). Separation yields
dx
x
=
−
dt
⇒
ln

x

=
−
t
+
C
⇒
x
(
t
)=
c
2
e
−
t
.
Substituting this solution into the second equation, we obtain an equation for
y
:
y
0
+2
y
=
x
=
c
2
e
−
t
.
This equation is a Frst order linear equation. Solving we obtain
µ
(
t
)=exp
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This note was uploaded on 03/29/2010 for the course MATH 54257 taught by Professor Hald,oh during the Spring '10 term at University of California, Berkeley.
 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations

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