1550078481-Ordinary_Differential_Equations__Roberts_

The Initial Value Problem y' = f(x, y); y(c) = d 43 We state the following existence theorem without proof. This theorem is due ...

44 Ordinary Differential Equations EXAMPLE 1 An Initial Value Problem for which the Interval of Existence Depends on the Initial ...

4 2 y(x) O 2 -4 The Initial Value Problem y' = f(x, y); y(c) = d 1111111111 111111111 }~}}}}}}}}~}}}}~}}}~ j j j j j j j j j j ...

46 Ordinary Differential Equations FUNDAMENTAL EXISTENCE AND UNIQUENESS THEOREM Let R = {(x,y)i a< x < /3 and / < y < ...

The Initial Value Problem y' = f(x, y); y(c) = d 47 I EXAMPLE 2 The IVP y' = x.jY; y(c) = d Analyze initial value problems of th ...

48 Ordinary Differential Equations If f(x, y) and fy(x, y) are both defined and continuous on a finite rectangle, the rectangle ...

The Initial Value Problem y' = f(x, y); y(c) = d 49 from t he point (b, B). The solution Y2(x) is unique on the interval (e, +oo ...

50 4 2 y(x) O 2 -4 Ordinary Differential Equations I I I , I ~~~~~~~}}}}}~~~~~~~} j j j j j j j j j j j ~ j j j j j j j j //// ...

The Initial Value Problem y' = f(x, y); y(c) = d 51 boundary of the rectangle twice instead of two different boundaries. T he di ...

52 Ordinary Differential Equations and continuous functions of x on (a, (3) is reached. For linear initial value problems, it is ...

The Initial Value Problem y' = f(x, y); y(c) = d 53 SOLUTION a. The functions a(x) = 3x^2 and b(x) =ex are both defined and cont ...

54 Ordinary Differential Equations In exercises 7-12 find all points ( c , d) where solutions to the initial value problem consi ...

The Initial Value Problem y' = f(x, y); y(c) = d 55 2.3 Solution of Simple First-Order Differential Equations Sometimes one can ...

56 Ordinary Differential Equations b. Solve the initial value problem I 1 Y = (x + 2); y(l) =^4 and specify the interva l on whi ...

The Initial Value Problem y' = f(x, y); y(c) = d 57 we set x = - 7 in the general solution ( 4), solve the resulting equation fo ...

58 Ordinary Differential Equations 2.3.2 Solution of the Separable Equation y' = g(x)/h(y) From your study of calculus, you are ...

The Initial Value Problem y' = f(x, y); y(c) = d 59 variables." Once an equation is in the form (9), the process of separating v ...

60 Ordinary Differential Equations constants can be combined by subtraction into the single constant, C = c2 -c1. In addition, s ...

The Initial Value Problem y' = f(x, y) ; y(c) = d 61 2 y 2 y x -K K x -2 -K - 1 (^0) K (^2) -2 -1 0 2 -1 -1 -2 - 2 (a) (b) Figur ...

62 Ordinary Differential Equations EXAMPLE 3 Solving an IVP Using Separation of Variables Solve the initial value problem (18) y ...