1550078481-Ordinary_Differential_Equations__Roberts_

The Initial Value Problem y' = f(x, y); y(c) = d 63 where K is any arbitrary real constant. Since the initial condition, y(O) = ...

64 Ordinary Differential Equations 2.3.3 Solution of the Linear Equation y' = a(x)y + b(x) Throughout this subsection, we will a ...

The Initial Value Problem y' = f(x, y); y(c) = d 65 THEOREM SOLUTION OF THE HOMOGENEOUS LINEAR FIRST-ORDER DIFFERENTIAL EQUATION ...

66 Ordinary Differential Equations Next, we consider the nonhomogeneous linear first-order differential equa- tion (28) y' = a(x ...

The Initial Value Problem y' = f(x, y); y(c) = d 67 we obtain the function (30) Yi(x) = ef a(x)dx_ Remember that y 1 (x) is a so ...

68 Ordinary Differential Equations THEOREM SOLUTION OF THE NONHOMOGENEOUS LINEAR FIRST-ORDER DIFFERENTIAL EQUATION If a(x) and b ...

The faitial Value Problem y' = f(x, y); y(c) = d 69 SOLUTION a. In this instance, the function a( x) = tan x is defined and cont ...

70 Ordinary Differential Equations Hence, if T(t) is the temperature of the body at time t and A is the temper- ature of the sur ...

The Initial Value Problem y' = f(x, y); y(c) = d 71 Solving the right-hand equation for e^2 k, we find 2 k^175 -^65 llO^22 e = 1 ...

72 Ordinary Differential Equations y' = y/(x -1) +x^2 ; y(O) = 1 y' = y/x + sinx^2 ; y(-1) = -1 1 y(l) = 2 y' = (cotx)y + sin ...

The Initial Value Problem y' = f(x, y); y(c) = d 73 2.4 Numerical Solution The oldest and simplest algorithm for generating a nu ...

74 Ordinary Differential Equations In the late nineteenth century and early twentieth century, several com- mercially viable mec ...

The Initial Value Problem y' = J(x, y); y(c) = d 75 a finite set of rational numbers can be represented exactly and they are not ...

76 Ordinary Differential Equations finite rectangle in the xy-plane will guarantee that the IVP (1) has a unique solution ¢(x) o ...

The Initial Value Problem y' = f(x, y); y(c) = d 77 Observe that the absolute error at Xi is the vertical distance between the p ...

78 Ordinary Differential Equations 2.4.1 Single-Step Methods For single-step methods, it is convenient to symbolize the numerica ...

The Initial Value Problem y' = f(x, y); y(c) = d 79 and the discretization error, truncation error, or formula error for this me ...

80 Ordinary Differential Equations Substituting these expressions into equation (5) with m = 3 and hn = .1, we obtain the recurs ...

The Initial Value Problem y' = f(x, y); y(c) = d 81 on the interval [O, l]. 1 1 IEI :S: 4 , max lfC^3 l(x, y)l(.1)^4 < 1 9(.1 ...

82 Ordinary Differential Equations without having to calculate higher order derivatives. As a matter of fact, an approximation t ...