Question

A Habit to Acquire For each of the nonlinear systems in Problems 10-13, make a graph of the nullclines with arrows on and between them showing the direction of solutions. Iden- tify each equilibrium and label it stable or unstable. Interpret these sketches in terms of the systems' phase portraits, shown in Fig. 7.1.1(a)-(d), to clarify the behaviors of the trajecto- ries. Then for each graph write a paragraph to describe the behaviors. 10. $x' = y$ $y' = x(x - 1)$ 12. $x' = x^2 - y + 2$ $y' = y + 2x$ 11. $x' = xy$ $y' = y - 3 \cos x$ 13. $x' = 1 + y + x^2$ $y' = y/2 - 3x$

          A Habit to Acquire For each of the nonlinear systems in
Problems 10-13, make a graph of the nullclines with arrows
on and between them showing the direction of solutions. Iden-
tify each equilibrium and label it stable or unstable. Interpret
these sketches in terms of the systems' phase portraits, shown
in Fig. 7.1.1(a)-(d), to clarify the behaviors of the trajecto-
ries. Then for each graph write a paragraph to describe the
behaviors.
10. $x' = y$
$y' = x(x - 1)$
12. $x' = x^2 - y + 2$
$y' = y + 2x$
11. $x' = xy$
$y' = y - 3 \cos x$
13. $x' = 1 + y + x^2$
$y' = y/2 - 3x$

A Habit to Acquire For each of the nonlinear systems in
Problems 10-13, make a graph of the nullclines with arrows
on and between them showing the direction of solutions. Iden-
tify each equilibrium and label it stable or unstable. Interpret
these sketches in terms of the systems' phase portraits, shown
in Fig. 7.1.1(a)-(d), to clarify the behaviors of the trajecto-
ries. Then for each graph write a paragraph to describe the
behaviors.
10. x' = y
y' = x(x - 1)
12. x' = x^2 - y + 2
y' = y + 2x
11. x' = xy
y' = y - 3 cos x
13. x' = 1 + y + x^2
y' = y/2 - 3x

Added by Darlene W.

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