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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 first one, we eliminate
y
and obtain
x
+
y
=
−
2
y,
y
=
x
−
2
y
⇒
x
=
−
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
+ 2
y
=
x
=
c
2
e
−
t
.
This equation is a first order linear equation. Solving we obtain
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- Spring '10
- Hald,OH
- Math, Differential Equations, Linear Algebra, Algebra, Equations, Trigraph, Elementary algebra, order linear equation, phase plane analysis, c2 e−t e2t
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