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8th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781285740621

Chapter 9.2, Problem 6E

Textbook Problem

**3–6** Match the differential equation with its direction field (labeled I–IV). Give reasons for your answer.

Calculus (MindTap Course List)

Ch. 9.1 - Show that y=23ex+e2x is a solution of the...Ch. 9.1 - Verify that y=tcostt is a solution of the...Ch. 9.1 - a For what values of r does the function y=erx...Ch. 9.1 - a For what values of k does the function y=coskt...Ch. 9.1 - Which of the following functions are solutions of...Ch. 9.1 - a Show that every member of the family of...Ch. 9.1 - a What can you say about a solution of the...Ch. 9.1 - a What can you say about the graph of a solution...Ch. 9.1 - A population is modeled by the differential...Ch. 9.1 - The Fitzhugh-Nagumo model for the electrical...

Ch. 9.1 - Explain why the functions with the given graphs...Ch. 9.1 - The function with the given graph is a solution of...Ch. 9.1 - Match the differential equations with the solution...Ch. 9.1 - Suppose you have just poured a cup of freshly...Ch. 9.1 - Psychologists interested in learning theory study...Ch. 9.1 - Von Bertalanffys equation states that the rate of...Ch. 9.1 - Differential equations have been used extensively...Ch. 9.2 - A direction field for the differential equation...Ch. 9.2 - A direction field for the differential equation...Ch. 9.2 - 36 Match the differential equation with its...Ch. 9.2 - 36 Match the differential equation with its...Ch. 9.2 - 36 Match the differential equation with its...Ch. 9.2 - 36 Match the differential equation with its...Ch. 9.2 - Use the direction field labeled I above to sketch...Ch. 9.2 - Use the direction field labeled III above to...Ch. 9.2 - 910 Sketch a direction field for the differential...Ch. 9.2 - 910 Sketch a direction field for the differential...Ch. 9.2 - 1114 Sketch the direction field of the...Ch. 9.2 - 1114 Sketch the direction field of the...Ch. 9.2 - 1114 Sketch the direction field of the...Ch. 9.2 - 1114 Sketch the direction field of the...Ch. 9.2 - 1516 Use a computer algebra system to draw a...Ch. 9.2 - 1516 Use a computer algebra system to draw a...Ch. 9.2 - Use a computer algebra system to draw a direction...Ch. 9.2 - Make a rough sketch of a direction field for the...Ch. 9.2 - a Use Eulers method with each of the following...Ch. 9.2 - A direction field for a differential equation is...Ch. 9.2 - Use Eulers method with step size 0.5 to compute...Ch. 9.2 - Use Eulers method with step size 0.2 to estimate...Ch. 9.2 - Use Eulers method with step size 0.1 to estimate...Ch. 9.2 - a Use Eulers method with step size 0.2 to estimate...Ch. 9.2 - a Program a calculator or computer to use Eulers...Ch. 9.2 - a Program your computer algebra system, using...Ch. 9.2 - The figure shows a circuit containing an...Ch. 9.2 - In Exercise 9.1.14 we considered a 95C cup of...Ch. 9.3 - 110 Solve the differential equation. dydx=3x2y2Ch. 9.3 - 110 Solve the differential equation. dydx=xyCh. 9.3 - 110 Solve the differential equation. xyy=x2+1Ch. 9.3 - 110 Solve the differential equation. y+xey=0Ch. 9.3 - 110 Solve the differential equation. (ey1)y=2+cosxCh. 9.3 - 110 Solve the differential equation....Ch. 9.3 - 110 Solve the differential equation. ddt=tsecet2Ch. 9.3 - 110 Solve the differential equation....Ch. 9.3 - 110 Solve the differential equation. dpdt=t2pp+t21Ch. 9.3 - 110 Solve the differential equation. dzdt=et+z=0Ch. 9.3 - 1118 Find the solution of the differential...Ch. 9.3 - 1118 Find the solution of the differential...Ch. 9.3 - 1118 Find the solution of the differential...Ch. 9.3 - 1118 Find the solution of the differential...Ch. 9.3 - 1118 Find the solution of the differential...Ch. 9.3 - 1118 Find the solution of the differential...Ch. 9.3 - 1118 Find the solution of the differential...Ch. 9.3 - 1118 Find the solution of the differential...Ch. 9.3 - Find an equation of the curve that passes through...Ch. 9.3 - Find the function f such that...Ch. 9.3 - Solve the differential equation y=x+y by making...Ch. 9.3 - Solve the differential equation xy=y+xey/x by...Ch. 9.3 - a Solve the differential equation y=2x1y2. b Solve...Ch. 9.3 - Solve the equation eyy+cosx=0 and graph several...Ch. 9.3 - Solve the initial-value problem y=(sinx)/siny,...Ch. 9.3 - Solve the equation y=xx2+1/(yey) and graph several...Ch. 9.3 - a Use a computer algebra system to draw a...Ch. 9.3 - 2728 a Use a computer algebra system to draw a...Ch. 9.3 - 2932 Find the orthogonal trajectories of the...Ch. 9.3 - 2932 Find the orthogonal trajectories of the...Ch. 9.3 - 2932 Find the orthogonal trajectories of the...Ch. 9.3 - 2932 Find the orthogonal trajectories of the...Ch. 9.3 - 3335 An integral equation is an equation that...Ch. 9.3 - 3335 An integral equation is an equation that...Ch. 9.3 - 3335 An integral equation is an equation that...Ch. 9.3 - Find a function f such that f(3)=2 and...Ch. 9.3 - Solve the initial-value problem in Exercise 9.2.27...Ch. 9.3 - In Exercise 9.2.28 we discussed a differential...Ch. 9.3 - In Exercise 9.1.15 we formulated a model for...Ch. 9.3 - In an elementary chemical reaction, single...Ch. 9.3 - In contrast to the situation of Exercise 40,...Ch. 9.3 - A sphere with radius 1 m has temperature 15C. It...Ch. 9.3 - A glucose solution is administered intravenously...Ch. 9.3 - A certain small country has 10 billion in paper...Ch. 9.3 - A tank contains 1000 L of brine with 15 kg of...Ch. 9.3 - The air in a room with volume 180m3 contains 0.15...Ch. 9.3 - A vat with 500 gallons of beer contains 4 alcohol...Ch. 9.3 - A tank contains 1000 L of pure water. Brine that...Ch. 9.3 - When a raindrop falls, it increases in size and so...Ch. 9.3 - An object of mass m is moving horizontally through...Ch. 9.3 - Allometric growth in biology refers to...Ch. 9.3 - A model for tumor growth is given by the Gompertz...Ch. 9.3 - Let A(t) be the area of a tissue culture at time t...Ch. 9.3 - According to Newtons Law of Universal Gravitation,...Ch. 9.4 - 12 A population grows according to the given...Ch. 9.4 - 1-2 A population grows according to the given...Ch. 9.4 - Suppose that a population develops according to...Ch. 9.4 - Suppose that a population grows according to a...Ch. 9.4 - The Pacific halibut fishery has been modeled by...Ch. 9.4 - Suppose a population P(t) satisfies...Ch. 9.4 - Suppose a population grows according to a logistic...Ch. 9.4 - The table gives the number of yeast cells in a new...Ch. 9.4 - The population of the world was about 6.1 billion...Ch. 9.4 - a Assume that the carrying capacity for the US...Ch. 9.4 - One model for the spread of a rumor is that the...Ch. 9.4 - Biologists stocked a lake with 400 fish and...Ch. 9.4 - a Show that if P satisfies the logistic equation...Ch. 9.4 - For a fixed value of M say M=10, the family of...Ch. 9.4 - The table gives the midyear population of Japan,...Ch. 9.4 - The table gives the midyear population of Japan,...Ch. 9.4 - Consider a population P=P(t) with constant...Ch. 9.4 - Let c be a positive number. A differential...Ch. 9.4 - Lets modify the logistic differential equation of...Ch. 9.4 - Consider the differential equation...Ch. 9.4 - There is considerable evidence to support the...Ch. 9.4 - Another model for a growth function for a limited...Ch. 9.4 - In a seasonal-growth model, a periodic function of...Ch. 9.4 - Suppose we alter the differential equation in...Ch. 9.4 - Graphs of logistic functions Figures 2 and 3 look...Ch. 9.5 - 14 Determine whether the differential equation is...Ch. 9.5 - 14 Determine whether the differential equation is...Ch. 9.5 - 14 Determine whether the differential equation is...Ch. 9.5 - 14 Determine whether the differential equation is...Ch. 9.5 - 514 Solve the differential equation. y+y=1Ch. 9.5 - 514 Solve the differential equation. yy=exCh. 9.5 - 514 Solve the differential equation. y=xyCh. 9.5 - 514 Solve the differential equation....Ch. 9.5 - 514 Solve the differential equation. xy+y=xCh. 9.5 - 514 Solve the differential equation. 2xy+y=2xCh. 9.5 - 514 Solve the differential equation. xy2y=x2,x0Ch. 9.5 - 514 Solve the differential equation. y+2xy=1Ch. 9.5 - 514 Solve the differential equation....Ch. 9.5 - 514 Solve the differential equation....Ch. 9.5 - 1520 Solve the initial-value problem....Ch. 9.5 - 1520 Solve the initial-value problem....Ch. 9.5 - 1520 Solve the initial-value problem....Ch. 9.5 - 1520 Solve the initial-value problem....Ch. 9.5 - 1520 Solve the initial-value problem....Ch. 9.5 - 1520 Solve the initial-value problem....Ch. 9.5 - 2122 Solve the differential equation and use a...Ch. 9.5 - 2122 Solve the differential equation and use a...Ch. 9.5 - A Bernoulli differential equation named after...Ch. 9.5 - 2425 Use the method of Exercise 23 to solve the...Ch. 9.5 - 2425 Use the method of Exercise 23 to solve the...Ch. 9.5 - Solve the second-order equation xy+2y=12x2 by...Ch. 9.5 - In the circuit shown in Figure 4, a battery...Ch. 9.5 - In the circuit shown in Figure 4, a generator...Ch. 9.5 - The figure shows a circuit containing an...Ch. 9.5 - In the circuit of Exercise 29, R=2,C=0.01F,Q(0)=0...Ch. 9.5 - Let P(t) be the performance level of someone...Ch. 9.5 - Two new workers were hired for an assembly line....Ch. 9.5 - In Section 9.3 we looked at mixing problems in...Ch. 9.5 - A tank with a capacity of 400 L is full of a...Ch. 9.5 - An object with mass m is dropped from rest and we...Ch. 9.5 - If we ignore air resistance, we can conclude that...Ch. 9.5 - a Show that the substitution z=1/P transforms the...Ch. 9.5 - To account for seasonal variation in the logistic...Ch. 9.6 - For each predator-prey system, determine which of...Ch. 9.6 - Each system of differential equations is a model...Ch. 9.6 - The system of differential equations...Ch. 9.6 - Lynx eat snowshoe hares and snowshoe hares eat...Ch. 9.6 - 56 A phase trajectory is shown for populations of...Ch. 9.6 - 56 A phase trajectory is shown for populations of...Ch. 9.6 - 78 Graphs of populations of two species are shown....Ch. 9.6 - 78 Graphs of populations of two species are shown....Ch. 9.6 - In Example 1b we showed that the rabbit and wolf...Ch. 9.6 - Populations of aphids and ladybugs are modeled by...Ch. 9.6 - In Example 1 we used Lotka-Volterra equations to...Ch. 9.6 - In Exercise 10 we modeled populations of aphids...Ch. 9.R - a What is a differential equation? b What is the...Ch. 9.R - What can you say about the solutions of the...Ch. 9.R - What is a direction field for the differential...Ch. 9.R - Explain how Eulers method works.Ch. 9.R - What is a separable differential equation? How do...Ch. 9.R - What is a first-order linear differential...Ch. 9.R - a Write a differential equation that expresses the...Ch. 9.R - a Write the logistic differential equation. b...Ch. 9.R - a Write Lotka-Volterra equations to model...Ch. 9.R - Determine whether the statement is true or false....Ch. 9.R - Determine whether the statement is true or false....Ch. 9.R - Determine whether the statement is true or false....Ch. 9.R - Determine whether the statement is true or false....Ch. 9.R - Determine whether the statement is true or false....Ch. 9.R - Determine whether the statement is true or false....Ch. 9.R - Determine whether the statement is true or false....Ch. 9.R - a A direction field for the differential equation...Ch. 9.R - a Sketch a direction field for the differential...Ch. 9.R - a A direction field for the differential equation...Ch. 9.R - a Use Eulers method with step size 0.2 to estimate...Ch. 9.R - 58 Solve the differential equation. y=xesinxycosxCh. 9.R - 58 Solve the differential equation. dxdt=1t+xtxCh. 9.R - 58 Solve the differential equation. 2yey2y=2x+3xCh. 9.R - 58 Solve the differential equation. x2yy=2x3e1/xCh. 9.R - 911 Solve the initial-value problem....Ch. 9.R - 911 Solve the initial-value problem....Ch. 9.R - 911 Solve the initial-value problem....Ch. 9.R - Solve the initial-value problem y=3x2ey,y(0)=1,...Ch. 9.R - 1314 Find the orthogonal trajectories of the...Ch. 9.R - 13-14 Find the orthogonal trajectories of the...Ch. 9.R - a Write the solution of the initial-value problem...Ch. 9.R - a The population of the world was 6.1 billion in...Ch. 9.R - The von Bertalanffy growth model is used to...Ch. 9.R - A tank contains 100 L of pure water. Brine that...Ch. 9.R - One model for the spread of an epidemic is that...Ch. 9.R - The Brentano-Stevens Law in psychology models the...Ch. 9.R - The transport of a substance across a capillary...Ch. 9.R - Populations of birds and insects are modeled by...Ch. 9.R - Suppose the model of Exercise 22 is replaced by...Ch. 9.R - Barbara weighs 60 kg and is on a diet of 1600...Ch. 9.P - Find all functions f such that f is continuous and...Ch. 9.P - A student forgot the Product Rule for...Ch. 9.P - Let f be a function with the property that f(0)=1,...Ch. 9.P - Find all functions f that satisfy the equation...Ch. 9.P - Find the curve y=f(x) such that f(x)0, f(0)=0,...Ch. 9.P - A subtangent is a portion of the x-axis that lies...Ch. 9.P - A peach pie is taken out of the oven at 5:00 PM....Ch. 9.P - Snow began to fall during the morning of February...Ch. 9.P - A dog sees a rabbit running in a straight line...Ch. 9.P - a Suppose that the dog in Problem 9 runs twice as...Ch. 9.P - A planning engineer for a new alum plant must...Ch. 9.P - Find the curve that passes through the point 3, 2...Ch. 9.P - Recall that the normal line to a curve at a point...Ch. 9.P - Find all curves with the property that if the...Ch. 9.P - Find all curves with the property that if a line...Ch. 9.P - a An outfielder fields a baseball 280 ft away from...

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