Consider the equation a y ″ + b y ′ + c y = d , where a , b , c and d are constants. (a) Find all equilibrium, or constant, solutions of this differential equation. (b) Let y e denote an equilibrium solution, and let Y = y − y e . Thus Y is the deviation of a solution y from an equilibrium solution. Find the differential equation satisfied by Y .
Consider the equation a y ″ + b y ′ + c y = d , where a , b , c and d are constants. (a) Find all equilibrium, or constant, solutions of this differential equation. (b) Let y e denote an equilibrium solution, and let Y = y − y e . Thus Y is the deviation of a solution y from an equilibrium solution. Find the differential equation satisfied by Y .
Consider the equation
a
y
″
+
b
y
′
+
c
y
=
d
, where
a
,
b
,
c
and
d
are constants.
(a) Find all equilibrium, or constant, solutions of this differential equation.
(b) Let
y
e
denote an equilibrium solution, and let
Y
=
y
−
y
e
. Thus
Y
is the deviation of a solution
y
from an equilibrium solution. Find the differential equation satisfied by
Y
.
x
The function f is shown below. If I is the function defined by g(x) = √ ƒ(t) dt, find the value of g"(-8) in simplest form.
g
-1
8
y
7
10
6
LC
5
4
3 2
1
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
1
2
3
-1
-2
-3
-4
-5
56
-6
-7
-8
4 5
Graph of f
10
6
00
7 8
9 10
x
In Problems 1-16 the indicated function y₁(x) is a solution of the
given differential equation. Use reduction of order or formula (5), as
instructed, to find a second solution y2(x).
1. y" - 4y' + 4y = 0; yı
=
e2x
The function f is shown below. If g is an antiderivative of f such that g(6) = 2, what is the maximum value of g on the closed interval
[-9,9]?
8
7
6
Сл
5
4
3
1
y
Graph of f
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
1
23 4
-1
-2
-3
-4
-6
56
-5
-7
-8
LO
5
9
7
8
9
10
Chapter 4 Solutions
Differential Equations: An Introduction To Modern Methods And Applications 3e Binder Ready Version + Wileyplus Registration Card
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