Calculus, Early Transcendentals
Calculus, Early Transcendentals
9th Edition
ISBN: 9781337613927
Author: Stewart
Publisher: CENGAGE L
bartleby

Concept explainers

Differential Equations
Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…
bartleby

Videos

Textbook Question
Book Icon
Chapter 9.1, Problem 7E

Determine whether the given function is a solution of the differential equation.

7. y = 2 3 e x + e − 2 x ;   y ′ + 2 y = 2 e x

Expert Solution & Answer
Check Mark

Want to see the full answer?

Check out a sample textbook solution
Blurred answer
Previous
Chapter 9.1, Problem 6E
Next
Chapter 9.1, Problem 8E
Students have asked these similar questions
For each given function f(x) find f'(x) using the rules learned in section 9.5. 1. f(x)=x32 32x 2. f(x)=7x+13 3. f(x) = x4 4. f(x) = √√x³ 5. f(x) = 3x²+ 3 x2
Find: lim x →-6 f (x) limx-4 f (x) lim x-1 f (x) lim x →4 f (x) (-6,3) • (-1,5) -8 -7 (-6,-2) 4+ (4,5) (4,2) • (-1,1) -6
3 2 Find: ƒ(1) lim f(x) 14-x 2 ƒ(2) lim f(x) x-2- lim f(x) x+2+ lim f(x) x→4 3 y=f(x)

Chapter 9 Solutions

Calculus, Early Transcendentals

Ch. 9.1 - Write a differential equation that models the...Ch. 9.1 - Write a differential equation that models the...Ch. 9.1 - Prob. 3ECh. 9.1 - Prob. 4ECh. 9.1 - Prob. 5ECh. 9.1 - Determine whether the given function is a solution...Ch. 9.1 - Determine whether the given function is a solution...Ch. 9.1 - Prob. 9ECh. 9.1 - Prob. 12ECh. 9.1 - Show that the given function is a solution of the...
Ch. 9.1 - Prob. 14ECh. 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 = cos...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 y'...Ch. 9.2 - A direction field for the differential equation...Ch. 9.2 - Match the differential equation with its direction...Ch. 9.2 - Match the differential equation with its direction...Ch. 9.2 - Match the differential equation with its direction...Ch. 9.2 - Match the differential equation with its direction...Ch. 9.2 - Prob. 7ECh. 9.2 - Use the direction field labeled III (above) to...Ch. 9.2 - Sketch a direction field for the differential...Ch. 9.2 - Sketch a direction field for the differential...Ch. 9.2 - Prob. 11ECh. 9.2 - Prob. 12ECh. 9.2 - Prob. 13ECh. 9.2 - Prob. 14ECh. 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 - Prob. 22ECh. 9.2 - Prob. 23ECh. 9.2 - (a) Use Eulers method with step size 0.2 to...Ch. 9.2 - The figure shows a circuit containing an...Ch. 9.3 - Solve the differential equation. 1. dydx=3x2y2Ch. 9.3 - Solve the differential equation. 2. dydx=xy4Ch. 9.3 - Solve the differential equation. 2. dydx=xyCh. 9.3 - Solve the differential equation. 4. xy=y+3Ch. 9.3 - Solve the differential equation. 3. xyy=x2+1Ch. 9.3 - Solve the differential equation. 4. y+xey=0Ch. 9.3 - Solve the differential equation. 5. (ey1)y=2+cosxCh. 9.3 - Solve the differential equation. 8. dydx=2xy2+1Ch. 9.3 - Solve the differential equation. 9. dpdt=t2pp+t21Ch. 9.3 - Solve the differential equation. 10. dzdt+et+z=0Ch. 9.3 - Find the solution of the differential equation...Ch. 9.3 - Find the solution of the differential equation...Ch. 9.3 - Prob. 15ECh. 9.3 - Find the solution of the differential equation...Ch. 9.3 - Find the solution of the differential equation...Ch. 9.3 - Find the solution of the differential equation...Ch. 9.3 - Find the solution of the differential equation...Ch. 9.3 - Find an equation of the curve that passes through...Ch. 9.3 - Find the function f such that f(x) = xf(x) x and...Ch. 9.3 - Solve the differential equation y = x + y by...Ch. 9.3 - Solve the differential equation xy = y + xey/x by...Ch. 9.3 - (a) Solve the differential equation y=2x1y2. (b)...Ch. 9.3 - Solve the equation eyy + cos x = 0 and graph...Ch. 9.3 - Find the orthogonal trajectories of the family of...Ch. 9.3 - Find the orthogonal trajectories of the family of...Ch. 9.3 - Find the orthogonal trajectories of the family of...Ch. 9.3 - Find the orthogonal trajectories of the family of...Ch. 9.3 - Find a function f such that f(3) = 2 and (t2 +...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 an elementary chemical reaction, single...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 180 m3 contains...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 - An object of mass m is moving horizontally through...Ch. 9.3 - A model for tumor growth is given by the Gompertz...Ch. 9.3 - Prob. 1APCh. 9.3 - Prob. 2APCh. 9.4 - A population grows according to the given logistic...Ch. 9.4 - A population grows according to the given logistic...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 population of the world was about 6.1 billion...Ch. 9.4 - Prob. 10ECh. 9.4 - Prob. 11ECh. 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 - Consider a population P = P(t) with constant...Ch. 9.4 - Prob. 21ECh. 9.4 - In a seasonal-growth model, a periodic function of...Ch. 9.4 - Prob. 24ECh. 9.4 - Prob. 25ECh. 9.5 - Determine whether the differential equation is...Ch. 9.5 - Determine whether the differential equation is...Ch. 9.5 - Determine whether the differential equation is...Ch. 9.5 - Determine whether the differential equation is...Ch. 9.5 - Solve the differential equation. 5. y' + y = 1Ch. 9.5 - Solve the differential equation. 6. y' y = exCh. 9.5 - Solve the differential equation. 7. y' = x yCh. 9.5 - Solve the differential equation. 8. 4x3y + x4y' =...Ch. 9.5 - Solve the differential equation. 9. xy+y=xCh. 9.5 - Solve the differential equation. 10. 2xy+y=2xCh. 9.5 - Solve the differential equation. 11. xy2y=x2,x0Ch. 9.5 - Solve the differential equation. 12. y3x2y=x2Ch. 9.5 - Solve the differential equation. 13....Ch. 9.5 - Solve the differential equation. 14....Ch. 9.5 - Solve the differential equation. 15. y+ycosx=xCh. 9.5 - Solve the differential equation. 16. y+2xy=x3ex2Ch. 9.5 - Solve the initial-value problem. 17....Ch. 9.5 - Solve the initial-value problem. 18....Ch. 9.5 - Solve the initial-value problem. 15....Ch. 9.5 - Solve the initial-value problem. 16....Ch. 9.5 - Solve the initial-value problem. 17....Ch. 9.5 - Solve the initial-value problem. 18....Ch. 9.5 - Solve the initial-value problem. 19....Ch. 9.5 - Solve the initial-value problem. 20....Ch. 9.5 - Solve the differential equation and use a...Ch. 9.5 - Prob. 26ECh. 9.5 - Bernoulli Differential Equations A Bernoulli...Ch. 9.5 - Bernoulli Differential Equations A Bernoulli...Ch. 9.5 - Bernoulli Differential Equations A Bernoulli...Ch. 9.5 - Solve the second-order equation xy" + 2y' = 12x2...Ch. 9.5 - Prob. 31ECh. 9.5 - Prob. 32ECh. 9.5 - The figure shows a circuit containing an...Ch. 9.5 - Prob. 34ECh. 9.5 - Prob. 35ECh. 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 - Prob. 40ECh. 9.5 - Show that the substitution z = 1/P transforms the...Ch. 9.5 - Prob. 42ECh. 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 - Prob. 4ECh. 9.6 - Prob. 5ECh. 9.6 - Prob. 6ECh. 9.6 - Prob. 7ECh. 9.6 - Graphs of populations of two species are shown....Ch. 9.6 - Populations of aphids and ladybugs are modeled by...Ch. 9.6 - Prob. 11ECh. 9 - (a) What is a differential equation? (b) What is...Ch. 9 - What can you say about the solutions of the...Ch. 9 - What is a direction field for the differential...Ch. 9 - Explain how Euler's method works.Ch. 9 - What is a separable differential equation? How do...Ch. 9 - What is a first-order linear differential...Ch. 9 - (a) Write a differential equation that expresses...Ch. 9 - (a) Write the logistic differential equation. (b)...Ch. 9 - (a) Write Lotka-Volterra equations to model...Ch. 9 - Determine whether the statement is true or false....Ch. 9 - Determine whether the statement is true or false....Ch. 9 - Determine whether the statement is true or false....Ch. 9 - Determine whether the statement is true or false....Ch. 9 - Determine whether the statement is true or false....Ch. 9 - Prob. 7TFQCh. 9 - Determine whether the statement is true or false....Ch. 9 - (a) A direction field for the differential...Ch. 9 - (a) Sketch a direction field for the differential...Ch. 9 - (a) A direction field for the differential...Ch. 9 - (a) Use Euler's method with step size 0.2 to...Ch. 9 - Solve the differential equation. 5. y=xesinxycosxCh. 9 - Solve the differential equation. 6. dxdy=1t+xtxCh. 9 - Solve the differential equation. 7. 2yey2y=2x+3xCh. 9 - Solve the differential equation. 8. x2yy=2x3e1/xCh. 9 - Solve the initial-value problem. 9....Ch. 9 - Solve the initial-value problem. 10. (1 + cos x)...Ch. 9 - Solve the initial-value problem. 11. xy' y = x ln...Ch. 9 - Solve the initial-value problem y' = 3x2ey, y(0) =...Ch. 9 - Find the orthogonal trajectories of the family of...Ch. 9 - Find the orthogonal trajectories of the family of...Ch. 9 - (a) Write the solution of the initial-value...Ch. 9 - The von Bertalanffy growth model is used to...Ch. 9 - A tank contains 100 L of pure water. Brine that...Ch. 9 - One model for the spread of an epidemic is that...Ch. 9 - The Brentano-Stevens Law in psychology models the...Ch. 9 - The transport of a substance across a capillary...Ch. 9 - Populations of birds and insects are modeled by...Ch. 9 - Suppose the model of Exercise 22 is replaced by...Ch. 9 - Barbara weighs 60 kg and is on a diet of 1600...Ch. 9 - Find all functions f such that f' is continuous...Ch. 9 - A student forgot the Product Rule for...Ch. 9 - Let f be a function with the property that f(0) =...Ch. 9 - Find all functions f that satisfy the equation...Ch. 9 - Find the curve y = f(x) such that f(x) 0, f(0) =...Ch. 9 - A subtangent is a portion of the x-axis that lies...Ch. 9 - A peach pie is taken out of the oven at 5:00 pm....Ch. 9 - Snow began to fall during the morning of February...Ch. 9 - (a) Suppose that the dog in Problem 9 runs twice...Ch. 9 - A planning engineer for a new alum plant must...Ch. 9 - Find the curve that passes through the point (3,...Ch. 9 - Recall that the normal line to a curve at a point...Ch. 9 - Find all curves with the properly that if the...Ch. 9 - Find all curves with the property that if a line...
Knowledge Booster
Background pattern image
Calculus
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Calculus: Early Transcendentals
Calculus
ISBN:9781285741550
Author:James Stewart
Publisher:Cengage Learning
Text book image
Thomas' Calculus (14th Edition)
Calculus
ISBN:9780134438986
Author:Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:PEARSON
Text book image
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:9780134763644
Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:PEARSON
Text book image
Calculus: Early Transcendentals
Calculus
ISBN:9781319050740
Author:Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:W. H. Freeman
Text book image
Precalculus
Calculus
ISBN:9780135189405
Author:Michael Sullivan
Publisher:PEARSON
Text book image
Calculus: Early Transcendental Functions
Calculus
ISBN:9781337552516
Author:Ron Larson, Bruce H. Edwards
Publisher:Cengage Learning
SEE MORE TEXTBOOKS
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY
Solution of Differential Equations and Initial Value Problems; Author: Jefril Amboy;https://www.youtube.com/watch?v=Q68sk7XS-dc;License: Standard YouTube License, CC-BY