Fundamentals of Differential Equations (9th Edition)
9th Edition
ISBN: 9780321977069
Author: R. Kent Nagle, Edward B. Saff, Arthur David Snider
Publisher: PEARSON
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2. The table shows the population of waterfowl at a particular lake for selected years between
2002 and 2023. Which of the following equations shown best models the data in the table,
where y is the percent of households with computers and x is the number of years after
2000?
x
2002
2004
2011
2015
2018
2021
2023
y
585
582
629
726
873
1070
1317
A. y = 2.75x² + 36.9x + 669
B. y = 2.75 + 11041x + 669
C. y = 2.75x²11041x + 669
D. y = 2.75x² - 36.9x + 669
.2
dt
t2 + 1
#3
Chapter 1 Solutions
Fundamentals of Differential Equations (9th Edition)
Ch. 1.1 - In Problems 112, a differential equation is given...Ch. 1.1 - In Problems 112, a differential equation is given...Ch. 1.1 - In Problems 112, a differential equation is given...Ch. 1.1 - In Problems 112, a differential equation is given...Ch. 1.1 - In Problems 112, a differential equation is given...Ch. 1.1 - In Problems 112, a differential equation is given...Ch. 1.1 - In Problems 112, a differential equation is given...Ch. 1.1 - In Problems 112, a differential equation is given...Ch. 1.1 - Prob. 9ECh. 1.1 - In Problems 112, a differential equation is given...
Ch. 1.1 - In Problems 112, a differential equation is given...Ch. 1.1 - Prob. 12ECh. 1.1 - In Problems 1316, write a differential equation...Ch. 1.1 - In Problems 1316, write a differential equation...Ch. 1.1 - In Problems 1316, write a differential equation...Ch. 1.1 - In Problems 1316, write a differential equation...Ch. 1.1 - Prob. 17ECh. 1.2 - (a) Show that (x) = x2 is an explicit solution to...Ch. 1.2 - (a) Show that y2 + x 3 = 0 is an implicit...Ch. 1.2 - In Problems 38, determine whether the given...Ch. 1.2 - In Problems 38, determine whether the given...Ch. 1.2 - In Problems 38, determine whether the given...Ch. 1.2 - In Problems 38, determine whether the given...Ch. 1.2 - In Problems 38, determine whether the given...Ch. 1.2 - In Problems 38, determine whether the given...Ch. 1.2 - In Problems 913, determine whether the given...Ch. 1.2 - In Problems 913, determine whether the given...Ch. 1.2 - In Problems 913, determine whether the given...Ch. 1.2 - In Problems 913, determine whether the given...Ch. 1.2 - In Problems 913, determine whether the given...Ch. 1.2 - Prob. 14ECh. 1.2 - Verify that (x) = 2/(1 cex), where c is an...Ch. 1.2 - Verify that x2 + cy2 = 1, where c is an arbitrary...Ch. 1.2 - Show that (x) = Ce3x + 1 is a solution to dy/dx ...Ch. 1.2 - Let c 0. Show that the function (x) = (c2 x2) 1...Ch. 1.2 - Prob. 19ECh. 1.2 - Determine for which values of m the function (x) =...Ch. 1.2 - Prob. 21ECh. 1.2 - Prob. 22ECh. 1.2 - Prob. 23ECh. 1.2 - In Problem 2328, determine whether Theorem 1...Ch. 1.2 - In Problem 2328, determine whether Theorem 1...Ch. 1.2 - (a) Find the total area between f(x) = x3 x and...Ch. 1.2 - In Problem 2328, determine whether Theorem 1...Ch. 1.2 - In Problem 2328, determine whether Theorem 1...Ch. 1.2 - (a) For the initial value problem (12) of Example...Ch. 1.2 - Prob. 30ECh. 1.2 - Consider the equation of Example 5, (13)ydydx4x=0....Ch. 1.3 - The direction field for dy/dx = 4x/y is shown in...Ch. 1.3 - Prob. 2ECh. 1.3 - A model for the velocity at time t of a certain...Ch. 1.3 - Prob. 4ECh. 1.3 - The logistic equation for the population (in...Ch. 1.3 - Consider the differential equation dydx=x+siny....Ch. 1.3 - Consider the differential equation dpdt=p(p1)(2p)...Ch. 1.3 - The motion of a set of particles moving along the...Ch. 1.3 - Let (x) denote the solution to the initial value...Ch. 1.3 - Use a computer software package to sketch the...Ch. 1.3 - Prob. 11ECh. 1.3 - Prob. 12ECh. 1.3 - Prob. 13ECh. 1.3 - In Problems 11-16, draw the isoclines with their...Ch. 1.3 - Prob. 15ECh. 1.3 - Prob. 16ECh. 1.3 - From a sketch of the direction field, what can one...Ch. 1.3 - Prob. 18ECh. 1.3 - Prob. 19ECh. 1.3 - Prob. 20ECh. 1.4 - In many of the problems below, it will be helpful...Ch. 1.4 - Prob. 2ECh. 1.4 - Prob. 3ECh. 1.4 - Prob. 4ECh. 1.4 - Prob. 5ECh. 1.4 - Use Eulers method with step size h = 0.2 to...Ch. 1.4 - Prob. 7ECh. 1.4 - Prob. 8ECh. 1.4 - Prob. 9ECh. 1.4 - Use the strategy of Example 3 to find a value of h...Ch. 1.4 - Prob. 11ECh. 1.4 - Prob. 12ECh. 1.4 - Prob. 13ECh. 1.4 - Prob. 14ECh. 1.4 - Prob. 15ECh. 1.4 - Prob. 16ECh. 1 - In Problems 16, identify the independent variable,...Ch. 1 - Prob. 2RPCh. 1 - Prob. 3RPCh. 1 - Prob. 4RPCh. 1 - Prob. 5RPCh. 1 - Prob. 6RPCh. 1 - Prob. 7RPCh. 1 - Prob. 8RPCh. 1 - Prob. 9RPCh. 1 - Prob. 10RPCh. 1 - Prob. 11RPCh. 1 - Prob. 12RPCh. 1 - Prob. 13RPCh. 1 - Prob. 14RPCh. 1 - Prob. 15RPCh. 1 - Prob. 16RPCh. 1 - Prob. 17RPCh. 1 - Prob. 1TWECh. 1 - Compare the different types of solutions discussed...
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- 12. Is the data x representative of a linear, quadratic, or exponential model? x -3 -2 -1 0 -18 -6 -2 0 y O 1 2 2 3 6 18 linear quadratic exponential -3 -2 -2 -1 -1 0 1 y 18 -6 -2 0 2 * 1 2 6 × 18arrow_forward4 B = (-1,4) A A = (1,0.25) %3D -5 -4 -3 -2 1 5 A y= – 4× B y=4=x (금) " f(x) = D y=4•1* 4, 3. 2. 1. 2.arrow_forwardPls #14arrow_forward
- 10. State whether each equation is true or false. (a) (p + q)² = p² + q? (b) Jab Va o (c) va? + b² = a + b 1+ TC (d) = 1 + T C 1/x (f) a/x – b/x 1 1 1 X - y у а — barrow_forwardA study is made for a particular allergy medication in order to determine the length of relief it provides Y (in hours) in relation to the dosage of medication X (in mg). For this reason, ten patients were given different doses of the medication and were asked to report back when the medication seemed to wear off. Patient #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 Dosage (x) Relief Hours (y) 3 3.5 4 5 6 6.5 7 8 8.5 9 9.1 5.5 12.3 9.2 14.2 16.8 22.0 18.3 24.5 22.7 (i) Draw a scatter diagram. (ii) Calculate the product moment correlation coefficient and comment on your answer. (iii) Construct the least squares regression line.arrow_forwardQUESTION 2 In the linear model, E(Y1) = OA. B2 * X1. OB. B1. OC. B1 + B2*X1. D. none of the above. Click Save and Submit to save and submit. Click Save All Answers to save all answers. 9 esc 20 F3 םסא F1 F2 F4 F! @ $ 1 4 W E R ab # 3arrow_forward
- helparrow_forwardIn Problems 1 through 6, show directly that the given functions are linearly dependent on the real line. That is, find a non- trivial linear combination of the given functions that vanishes identically. 1. f(x) = 2x, g(x) = 3x², h(x) = 5x – 8x² 2. f(x) = 5, g(x) = 2 – 3x², h(x) = 10 + 15x2 3. f(x) = 0, g(x) = sin x, h(x) = e* 4. f(x) = 17, g(x) = 2 sin² x, h(x) = 3 cos? x 5. f(x) = 17, g(x) = cos² x, h(x) = cos 2x 6. f(x) = e*, g(x) = cosh x, h(x) = sinh x %3D %3Darrow_forward5). If you have a problem with one dependent variable and two independent ones, show how the errors in the independent variables will impact the dependent one. O dy A1 dx1 + A2 dx2 Ody-A1 dx1 + A2 (dx1)^2 O dy-dy/dx1 dx1 O dy dy/dx1 dx1+dy/dx2 dx2arrow_forward
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