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Unformatted text preview: Figures 30. y = Ce 4 x x 1 4 32. y 2 = x 2 ln( x 2 ) + 16 x 2 34. y = x 2 sin x + 2 x 2 2 36. sin(2 x + y ) x 3 3 + e y = sin 2 + 2 3 38. y = 2 1 4 arctan x 2 2 40. y = 8 1 3 e 4 x 4 x TABLES n x n y n n x n y n 1 0.1 1.475 6 0.6 1.353368921 2 0.2 1.4500625 7 0.7 1.330518988 3 0.3 1.425311875 8 0.8 1.308391369 4 0.4 1.400869707 9 0.9 1.287062756 5 0.5 1.376852388 10 1.0 1.266596983 Table 2A : Eulers approximations to y = x y , y (0) = 0, on [0 , 1] with h = 0 . 1. FIGURES K 1 1 2 3 y ( t ) 2 4 6 8 Figure 2A : The graph of the solution in Problem 28. 71 Chapter 2 K 3 K 2 1 2 3 K 3 K 2 K 1 1 2 3 Figure 2B : The direction field and solution curve in Problem 32. 2 4 6 K 1.0 K 0.5 0.5 1.0 Figure 2C : The graph of the solution in Problem 32. K 2 2 4 K 2 2 4 Figure 2D : Curves and their orthogonal trajectories in Problem 34. 72 CHAPTER 3: Mathematical Models and Numerical Methods Involving First Order Equations EXERCISES 3.2: Compartmental Analysis 2. Let x ( t ) denote the mass of salt in the tank at time t with t = 0 denoting the moment when the process started. Thus we have x (0) = 0 . 5 kg. We use the mathematical model described by equation (1) of the text to find...
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This note was uploaded on 02/12/2011 for the course MA 221 taught by Professor Mazmani during the Spring '08 term at Stevens.
 Spring '08
 MAZMANI
 Equations

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