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Calculus (MindTap Course List)

8th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781285740621

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BuyFindarrow_forward

Calculus (MindTap Course List)

8th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781285740621
Chapter 9.1, Problem 13E
Textbook Problem
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Match the differential equations with the solution graphs labeled I–IV. Give reasons for your choices.

(a) y = 1 + x 2 + y 2

(b) y = x e x 2 y 2

(a) y = 1 1 + e x 2 + y 2

(a) y = sin ( x y ) cos ( x y )

Chapter 9.1, Problem 13E, Match the differential equations with the solution graphs labeled IIV. Give reasons for your

To determine

To match:

The differential equation with the solution graphs and to give the reasons for choices.

Explanation of Solution

1) Concept:

i. From the graph of function see the nature of function.

ii. P is increasing if dPdt>0 and decreasing if dPdt<0

2) Given:

The differential equation y'=1+x2+y2

And the solution graphs are,

3) Calculation:

The given differential equation is

y'=1+x2+y2

And the graph of functions is

Consider y'=1+x2+y2

Notice that, y'=1+x2+y21 for all values of x & y and as x increases y' is also increases, as x, y'

From the above graph see that only graph with labelled III is satisfactory with this condition.

Therefore, the differential equation y'=1+x2+y2 matches with the solution graph labelled  III, because it is reasonable with the condition, as x, y'

Conclusion:

The differential equation y'=1+x2+y2 matches with the solution graph labelled  III, because it is reasonable with the condition, as x, y'

To match:

The differential equation with the solution graphs and to give the reasons for choices.

Solution:

The differential equation y'=xe-x2-y2 matches with the solution graph labelled  I, because it is only graph reasonable with the condition, y'>0 for x>0 and y'<0 if  x<0

1) Concept:

i. From the graph of function see the nature of function.

ii. P is increasing if dPdt>0 and decreasing if dPdt<0

2) Given:

The differential equation y'=xe-x2-y2 

And the solution graphs

3) Calculation:

The given differential equation is

y'=xe-x2-y2

And the graphs of functions are

Consider y'=xe-x2-y2

Notice that, y'=xe-x2-y2>0 for x>0 and y'=xe-x2-y2<0 if  x<0

From the above graph see that only function with negative tangent slope ( that is decreasing) when x<0 and positive tangent slope (increasing) when x>0 is function in graph labelled I

Therefore, the graph with labelled I is satisfactory with this condition.

Therefore, the differential equation y'=xe-x2-y2 matches with the solution graph labelled  I, because it is only graph reasonable with the condition, y'>0 for x>0 and y'<0 if  x<0

Conclusion:

The differential equation y'=xe-x2-y2 matches with the solution graph labelled  I, because it is only graph reasonable with the condition, y'>0 for x>0 and y'<0 if  x<0

To match:

The differential equation with the solution graphs and to give the reasons for choices.

Solution:

The differential equation y'=11+ex2+y2  matches with the solution graph labelled  IV, because it is only graph reasonable with the condition, y'>0 for x and y'0 as  x

1) Concept:

i. From the graph of function see the nature of function.

ii. P is increasing if  dPdt>0 and decreasing if  dPdt<0

2) Given:

The differential equation y'=11+ex2+y2 

And the solution graphs are

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Chapter 9 Solutions

Calculus (MindTap Course List)
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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. 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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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