1550078481-Ordinary_Differential_Equations__Roberts_

Introduction 23 At this point, we need to examine a few initial value problems and bound- ary value problems to determine whethe ...

24 Ordinary Differential Equations EXAMPLE 4 An Initial Value Problem with an Infinite Number of Solutions The differential equa ...

Introduction 25 EXAMPLE 6 An Initial Value Problem with an Infinite Number of Piecewise Defined Solutions One solution on the in ...

26 Ordinary Differential Equations Figure 1.4 Solutions Curves y = A sin x of y" + y = O; y(O) = 0 EXAMPLE 7 A Boundary Value Pr ...

Introduction 27 EXAMPLE 9 A Boundary Value Problem with an Infinite Number of Solutions As in the previous two examples, if the ...

28 Ordinary Differential Equations Show that for all a :::; 0 and a ll b 2 0 l (x - a)^3 , x < a :::; 0 Yab(x)= 0 , a:=;x:: ...

Introduction 29 1.4 A Nobel Prize Winning Application Generally a mathematical model is constructed to approximate a physical pr ...

30 Ordinary Differential Equations and (5) Evaluating equation (3) at t = t 0 and imposing the condition (4), we see the constan ...

Introduction 31 5568 years. Radioactive carbon is constantly being produced in the earth's upper atmosphere by incoming cosmic r ...

32 Ordinary Differential Equations in the past), the time that a particular sample of the same substance died can be calculated ...

Chapter 2 The Initial Value Problem y' = f(x, y); y(c) = d In this chapter we discuss in detail the first-order initial value pr ...

34 Ordinary Differential Equations In chapter 1 we gave examples of initial value problems with no solution, with a unique solut ...

The Initial Value Problem y' = f(x, y) ; y(c) = d 35 (3) If the direction lines immediately above and to the left of (x, y) have ...

36 Ordinary Differential Equations Notice that a solution which passes through any point below the line y = x-l is strictly incr ...

The Initial Value Problem y' = f(x, y); y(c) = d 37 \ \ 4 ~ ~ 2 ~ ~ ~ ~ \ \ y(x) 0 -2 -4 ~ ~ ~ ~ ~ ~ }. }. }. I I C=O -4 -2 c = ...

38 Ordinary Differential Equations and the x and y axes are to appear as a box outside of the rectangle (axes = BOXED ) instead ...

The Initial Value Problem y' = j(x, y); y(c) = d 39 I EXAMPLE 3 Direction Field for y' = .jXY Graph the direction field of the d ...

40 Ordinary Differ ential Equations EXERCISES 2.1 In exercises 1-5 match the given differential equations with their direction f ...

The Initial Value P roblem y' = f(x, y) ; y( c) = d 3. E. y' = y^2 -4 F. y' = 4 - y^2 4 llllllllllllllllllll 2 ((((((((((((((((( ...

42 Ordinary Differential Equations In exercises 6-17 graph the direction field of the given differential equation on the rectang ...