ELEMENTRY DIFFERENTIAL EQUATIONS
9th Edition, Boyce
Chapter 5.1
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7We need to determine the radius of convergence for the power series,
Apply the ratio test.
=
Since this limit is indeterminate of the form
of degree 2, we do this twice.
, we can us
ELEMENTRY DIFFERENTIAL EQUATIONS
9th Edition, Boyce
Chapter 3.8
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The general solution is
, where we have that
and
(a)
(b)
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The general solution is
, where we have that
and
(a)
(b)
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(a)
(b)
(c)
The amplitude for
ELEMENTRY DIFFERENTIAL EQUATIONS
CHAPTER 2
2.4 PROBLEMS
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19We use technology to draw a direction field and plot several solutions:
It appears that all solutions approach 0 asymptotically as t increases, regardless of their va
ELEMENTRY DIFFERENTIAL EQUATIONS
9th Edition, Boyce
Chapter 2.5
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(a) Consider the equation
dy/dt = k(1 - y)2, (Equation A)
where k is a positive constant. Show that y = 1 is the only critical point, with the
correspopnding equilibrium solution (t) =
ELEMENTRY DIFFERENTIAL EQUATIONS
9th Edition, Boyce
Chapter 2.7
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5We use technology to plot the direction field:
It appears that the solution is converges when y
0 undefined for y<0
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Given
Using the OED Architect
All solutions seem to diverge
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1