Thomas Calculus 13th [Solutions]

684 Chapter 9 First-Order Differential Equations
(b) There is a stable equilibrium at X N and an unstable equilibrium at X = 0.
2
d x 2
k dx ( N X ) kX dx k X ( N X ) ( N 2 X ) inflection point at
2
dt dt
dt
X 0, X N , and X N.
2
(c)
(d) The spread rate is most rapid when
19. L di Ri V di V R i R V i , V , L, R 0
dt dt L L L R
Equilibrium: di R V i 0 i V
dt L R R
2
Concavity: d i R di R
2
V i
2
dt L dt L R
Phase Line:
x N
2 . Eventually all of the people will receive the item.
If the switch is closed at t 0, then i (0) 0, and the graph of the solution looks like this:
As t , it i V
steady state . (In the steady state condition, the self-inductance acts like a simple wire
R
connector and, as a result, the current through the resistor can be calculated using the familiar version of
Ohms Law.)
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