4.1, First-Order Systems and Applications 235
i _ A solution of the system in (24) is an ntuple of functions x10), x2(t),'. - -,
x". (t) that (on some interval) identically satisfy each of the equations in (24). We
W111 see that the general theory of a s

3.4 MechanicolVibrorions 18-1
The following table compares the rst four values t1. t2, t3.t4 W6 03101113? for the undamped
and clamped cases, respectively. '
Accordingly, in Fig. 3.4.11 (where only the rst three equilibrium passages are shown) we
se

206
-Btoblsms
In Problems 1 through 6, express the solution of the given ini-
tial value problem as a sum of two oscillations as in Eq. (8)-
Throughout, primes denote derivatives with respect to time t.
In Problems [4, graph the solution function x(t) in

_ . S
Chapter 2 Mathematical Models and Numerical Method
= 200 into (15) gives B =
600e'006t
P(t)135107?
T = 1n(4)/0.06
has 0' Consequ
explosion.
(15) gives B =
82 4. With this value of B We solve
(a) Substitution oft = 0 and P
Eq. (15) for (16) _
~ 23.10

2.4 Numerical Approximation: Euler's Method 113
branch at a point of nonuniqueness). One should never accept as accurate the results
of applying Eulers method with a single xed step size h. A second run with
smaller step size (h / 2, say, or h/S, or h / 1

Homework 6
Tim Ryan
October 27, 2016
3.1.19: If y = 1 + x, then
3/2 1/2 2
x
x3/2
x
yy + (y ) = (1 + x)
+
=
6= 0.
4
2
4
00
0 2
3.1.29: There is no contradiction. If the given differential equation is divided by x2 , we get the
4
6
standard form of Equati