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nagle_differential_equations_ISM_Part16

# nagle_differential_equations_ISM_Part16 - Figures 30 y =...

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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 π 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 2–A : Euler’s approximations to y = x - y , y (0) = 0, on [0 , 1] with h = 0 . 1. FIGURES Figure 2–A : The graph of the solution in Problem 28. 71

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Chapter 2 Figure 2–B : The direction field and solution curve in Problem 32. Figure 2–C : The graph of the solution in Problem 32. Figure 2–D : 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 x ( t ). Since the solution is entering the tank with rate 6 L/min and contains 0 . 05 kg/L of salt, input rate = 6 (L / min) · 0 . 05 (kg / L) = 0 .

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nagle_differential_equations_ISM_Part16 - Figures 30 y =...

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