Answers to Selected Exercises
Chapter 1 INTRODUCTION
Exercises 1.2 D e finit ions a n d Terminology
Linear or
Order Nonlinear- 1 Linear
- 1 Nonlinear
5.^1 Nonlinear - 1 Linear
- 2 Nonlinear
- 2 Linear
- 3 Nonlinear
- a. No, y = l/x is not differentiable at 0.
b. Yes, y = l/x is differentiable on (0, oo) and satisfies the differential
equation on (0, oo).c. Yes, y = l/x is differentiable on (-oo, 0) and satisfies the differen-
tial equation on (-oo, 0).17. a. No, y = ,jX is not defined and not differentiable on (-1, 0).
b. Yes, y = ,jX is differentiable on (0, oo) and satisfies the differential
equation on (0, oo).
c. No, y = ,jX is not defined and not differentia ble on (-oo, 0).Intervals on which the solut io n exists.
(-oo, 0) (O,oo) 21. (0, 00)^23. (-oo, 0) (0, oo)
y 1 is a solution on (- 00,00). Y2 is a solution on (O,oo).
r = -3 29. r = -1 31. r = 1 /2 33. r = -4, r = -1
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