Calculus: An Applied Approach (MindTap Course List)
10th Edition
ISBN: 9781305860919
Author: Ron Larson
Publisher: Cengage Learning
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Question
Chapter 11, Problem 47RE
To determine
To calculate: The particular solution of the differential equation
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Differential Calculus: show solution
Mathematics
MATH 1001(001-081)
Question #9
Please answer the following.
a) Populations of birds and insects are modeled by
the differential equations shown below. Which
of the variables, x or y, represents the birds and
which represents the insects?
dx
= 0.4x-0.002xy
dt
dy = -0.2y+0.000008xy
dt
b) Please verify that y=4x-12x² +3 is a solution
to the differential equation y"-2xy' +8y = 0.
Chapter 11 Solutions
Calculus: An Applied Approach (MindTap Course List)
Ch. 11.1 - Checkpoint 1 Worked-out solution available at...Ch. 11.1 - Prob. 2CPCh. 11.1 - Prob. 3CPCh. 11.1 - Prob. 4CPCh. 11.1 - Prob. 1SWUCh. 11.1 - Prob. 2SWUCh. 11.1 - Prob. 3SWUCh. 11.1 - Prob. 4SWUCh. 11.1 - Prob. 5SWUCh. 11.1 - Prob. 6SWU
Ch. 11.1 - Verifying Solutions In Exercises 112, verify the...Ch. 11.1 - Prob. 2ECh. 11.1 - Prob. 3ECh. 11.1 - Prob. 4ECh. 11.1 - Prob. 5ECh. 11.1 - Prob. 6ECh. 11.1 - Prob. 7ECh. 11.1 - Prob. 8ECh. 11.1 - Verifying Solutions In Exercises 1-12, verify the...Ch. 11.1 - Prob. 10ECh. 11.1 - Prob. 11ECh. 11.1 - Prob. 12ECh. 11.1 - Prob. 13ECh. 11.1 - Prob. 14ECh. 11.1 - Determining Solutions In Exercises 1316, determine...Ch. 11.1 - Prob. 16ECh. 11.1 - Determining Solutions In Exercises 1720, determine...Ch. 11.1 - Prob. 18ECh. 11.1 - Prob. 19ECh. 11.1 - Prob. 20ECh. 11.1 - Prob. 21ECh. 11.1 - Prob. 22ECh. 11.1 - Prob. 23ECh. 11.1 - Prob. 24ECh. 11.1 - Prob. 25ECh. 11.1 - Prob. 26ECh. 11.1 - Prob. 27ECh. 11.1 - Prob. 28ECh. 11.1 - Prob. 29ECh. 11.1 - Prob. 30ECh. 11.1 - Prob. 31ECh. 11.1 - Prob. 32ECh. 11.1 - Prob. 33ECh. 11.1 - Prob. 34ECh. 11.1 - Prob. 35ECh. 11.1 - Prob. 36ECh. 11.1 - Prob. 37ECh. 11.1 - Prob. 38ECh. 11.1 - Prob. 39ECh. 11.1 - Investment The rate of growth of an investment is...Ch. 11.1 - Prob. 41ECh. 11.1 - Prob. 42ECh. 11.1 - Prob. 43ECh. 11.1 - Prob. 44ECh. 11.1 - Prob. 45ECh. 11.1 - Prob. 46ECh. 11.2 - Checkpoint 1 Worked-out solution available at...Ch. 11.2 - Prob. 2CPCh. 11.2 - Prob. 3CPCh. 11.2 - Prob. 4CPCh. 11.2 - Prob. 5CPCh. 11.2 - Prob. 6CPCh. 11.2 - Prob. 1SWUCh. 11.2 - Prob. 2SWUCh. 11.2 - Prob. 3SWUCh. 11.2 - Prob. 4SWUCh. 11.2 - Prob. 5SWUCh. 11.2 - Prob. 6SWUCh. 11.2 - Prob. 7SWUCh. 11.2 - Prob. 8SWUCh. 11.2 - Prob. 9SWUCh. 11.2 - Prob. 10SWUCh. 11.2 - Prob. 1ECh. 11.2 - Prob. 2ECh. 11.2 - Prob. 3ECh. 11.2 - Prob. 4ECh. 11.2 - Prob. 5ECh. 11.2 - Prob. 6ECh. 11.2 - Prob. 7ECh. 11.2 - Prob. 8ECh. 11.2 - Prob. 9ECh. 11.2 - Prob. 10ECh. 11.2 - Prob. 11ECh. 11.2 - Prob. 12ECh. 11.2 - Prob. 13ECh. 11.2 - Solving a Differential Equation In Exercises 7-26,...Ch. 11.2 - Prob. 15ECh. 11.2 - Prob. 16ECh. 11.2 - Prob. 17ECh. 11.2 - Prob. 18ECh. 11.2 - Prob. 19ECh. 11.2 - Prob. 20ECh. 11.2 - Prob. 21ECh. 11.2 - Prob. 22ECh. 11.2 - Prob. 23ECh. 11.2 - Prob. 24ECh. 11.2 - Prob. 25ECh. 11.2 - Prob. 26ECh. 11.2 - Prob. 27ECh. 11.2 - Prob. 28ECh. 11.2 - Prob. 29ECh. 11.2 - Prob. 30ECh. 11.2 - Prob. 31ECh. 11.2 - Finding a Particular Solution In Exercises 31-38,...Ch. 11.2 - Prob. 33ECh. 11.2 - Finding a Particular Solution In Exercises 31-38,...Ch. 11.2 - Prob. 35ECh. 11.2 - Finding a Particular Solution In Exercises 31-38,...Ch. 11.2 - Prob. 37ECh. 11.2 - Prob. 38ECh. 11.2 - Prob. 39ECh. 11.2 - Prob. 40ECh. 11.2 - Prob. 41ECh. 11.2 - Prob. 42ECh. 11.2 - Prob. 43ECh. 11.2 - Prob. 44ECh. 11.2 - Radioactive Decay The rate of decomposition of...Ch. 11.2 - Radioactive Decay The rate of decomposition of...Ch. 11.2 - Solve the differential equation. Weight Gain A...Ch. 11.2 - Prob. 1QYCh. 11.2 - Prob. 2QYCh. 11.2 - Prob. 3QYCh. 11.2 - Prob. 4QYCh. 11.2 - Prob. 5QYCh. 11.2 - Prob. 6QYCh. 11.2 - Prob. 7QYCh. 11.2 - Prob. 8QYCh. 11.2 - Prob. 9QYCh. 11.2 - Prob. 10QYCh. 11.2 - Prob. 11QYCh. 11.2 - Prob. 12QYCh. 11.2 - Prob. 13QYCh. 11.2 - Prob. 14QYCh. 11.2 - Prob. 15QYCh. 11.2 - Ignoring resistance, a sailboat starting from rest...Ch. 11.3 - Checkpoint 1 Worked-out solution available at...Ch. 11.3 - Prob. 2CPCh. 11.3 - Prob. 3CPCh. 11.3 - Prob. 1SWUCh. 11.3 - Prob. 2SWUCh. 11.3 - Prob. 3SWUCh. 11.3 - Prob. 4SWUCh. 11.3 - Prob. 5SWUCh. 11.3 - Prob. 6SWUCh. 11.3 - Prob. 7SWUCh. 11.3 - Prob. 8SWUCh. 11.3 - In Exercises 5-10, find the indefinite integral....Ch. 11.3 - Prob. 10SWUCh. 11.3 - Prob. 1ECh. 11.3 - Prob. 2ECh. 11.3 - Prob. 3ECh. 11.3 - Prob. 4ECh. 11.3 - Prob. 5ECh. 11.3 - Prob. 6ECh. 11.3 - Prob. 7ECh. 11.3 - Prob. 8ECh. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Prob. 10ECh. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Prob. 13ECh. 11.3 - Prob. 14ECh. 11.3 - Prob. 15ECh. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Prob. 17ECh. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Using Two Methods In Exercises 19-22, solve for y...Ch. 11.3 - Prob. 20ECh. 11.3 - Prob. 21ECh. 11.3 - Prob. 22ECh. 11.3 - Prob. 23ECh. 11.3 - Prob. 24ECh. 11.3 - Prob. 25ECh. 11.3 - Prob. 26ECh. 11.3 - Prob. 27ECh. 11.3 - Prob. 28ECh. 11.3 - Prob. 29ECh. 11.3 - Prob. 30ECh. 11.3 - Prob. 31ECh. 11.3 - Prob. 32ECh. 11.3 - Finding a Particular Solution In Exercises 27-34,...Ch. 11.3 - Prob. 34ECh. 11.3 - Prob. 35ECh. 11.3 - Prob. 36ECh. 11.3 - Vertical Motion A falling object encounters air...Ch. 11.3 - Velocity A booster rocket carrying an observation...Ch. 11.3 - Learning Curve The management at a medical supply...Ch. 11.3 - Investment Let A he the amount in a fund earning...Ch. 11.4 - Prob. 1CPCh. 11.4 - Prob. 2CPCh. 11.4 - Checkpoint 3 Worked-out solution available at...Ch. 11.4 - Prob. 4CPCh. 11.4 - Checkpoint 5 Worked-out solution available at...Ch. 11.4 - Prob. 1SWUCh. 11.4 - Prob. 2SWUCh. 11.4 - Prob. 3SWUCh. 11.4 - Prob. 4SWUCh. 11.4 - Prob. 5SWUCh. 11.4 - Prob. 6SWUCh. 11.4 - Prob. 7SWUCh. 11.4 - Prob. 8SWUCh. 11.4 - Prob. 9SWUCh. 11.4 - Prob. 10SWUCh. 11.4 - Prob. 1ECh. 11.4 - Prob. 2ECh. 11.4 - Advertising Awareness In Exercises 3 and 4, use...Ch. 11.4 - Prob. 4ECh. 11.4 - Prob. 5ECh. 11.4 - Prob. 6ECh. 11.4 - Prob. 7ECh. 11.4 - Prob. 8ECh. 11.4 - Prob. 9ECh. 11.4 - Prob. 10ECh. 11.4 - Prob. 11ECh. 11.4 - Prob. 12ECh. 11.4 - Prob. 13ECh. 11.4 - Prob. 14ECh. 11.4 - Prob. 15ECh. 11.4 - Prob. 16ECh. 11.4 - Prob. 17ECh. 11.4 - Chemistry A wet towel hung from a clothesline to...Ch. 11.4 - Prob. 19ECh. 11.4 - Prob. 20ECh. 11.4 - Biology A population of eight beavers has been...Ch. 11.4 - Prob. 22ECh. 11.4 - Prob. 23ECh. 11.4 - Prob. 24ECh. 11.4 - Chemical Mixture A 100-gallon tank is full of a...Ch. 11.4 - Chemical Mixture A 200-gallon tank is half full of...Ch. 11.4 - Prob. 29ECh. 11.4 - Prob. 30ECh. 11.4 - Prob. 31ECh. 11.4 - Prob. 32ECh. 11.4 - Prob. 33ECh. 11.4 - Prob. 34ECh. 11.4 - Prob. 35ECh. 11.4 - Prob. 36ECh. 11.4 - Prob. 37ECh. 11.4 - Prob. 38ECh. 11 - Prob. 1RECh. 11 - Prob. 2RECh. 11 - Prob. 3RECh. 11 - Prob. 4RECh. 11 - Prob. 5RECh. 11 - Prob. 6RECh. 11 - Prob. 7RECh. 11 - Prob. 8RECh. 11 - Prob. 9RECh. 11 - Prob. 10RECh. 11 - Prob. 11RECh. 11 - Prob. 12RECh. 11 - Prob. 13RECh. 11 - Prob. 14RECh. 11 - Finding a Particular Solution In Exercises 15 and...Ch. 11 - Prob. 16RECh. 11 - Prob. 17RECh. 11 - Prob. 18RECh. 11 - Prob. 19RECh. 11 - Prob. 20RECh. 11 - Prob. 21RECh. 11 - Prob. 22RECh. 11 - Prob. 23RECh. 11 - Prob. 24RECh. 11 - Prob. 25RECh. 11 - Prob. 26RECh. 11 - Prob. 27RECh. 11 - Prob. 28RECh. 11 - Prob. 29RECh. 11 - Prob. 30RECh. 11 - Prob. 31RECh. 11 - Prob. 32RECh. 11 - Prob. 33RECh. 11 - Prob. 34RECh. 11 - Prob. 35RECh. 11 - Prob. 36RECh. 11 - Prob. 37RECh. 11 - Prob. 38RECh. 11 - Prob. 39RECh. 11 - Prob. 40RECh. 11 - Prob. 41RECh. 11 - Solving a Differential Equation In Exercises...Ch. 11 - Prob. 43RECh. 11 - Prob. 44RECh. 11 - Prob. 45RECh. 11 - Prob. 46RECh. 11 - Prob. 47RECh. 11 - Prob. 48RECh. 11 - Prob. 49RECh. 11 - Prob. 50RECh. 11 - Prob. 51RECh. 11 - Prob. 52RECh. 11 - Prob. 53RECh. 11 - Prob. 54RECh. 11 - Prob. 55RECh. 11 - Prob. 56RECh. 11 - Solving a Linear Differential Equation In...Ch. 11 - Prob. 58RECh. 11 - Prob. 59RECh. 11 - Prob. 60RECh. 11 - Prob. 61RECh. 11 - Prob. 62RECh. 11 - Prob. 63RECh. 11 - Prob. 64RECh. 11 - Prob. 65RECh. 11 - Prob. 66RECh. 11 - Safety Assume the rate of change per hour in the...Ch. 11 - Prob. 68RECh. 11 - Prob. 69RECh. 11 - Prob. 70RECh. 11 - Prob. 71RECh. 11 - Prob. 72RECh. 11 - Prob. 73RECh. 11 - Prob. 74RECh. 11 - Prob. 75RECh. 11 - Chemical Mixture A tank contains 30 gallons of a...Ch. 11 - Chemical Mixture A tank contains 20 gallons of a...Ch. 11 - Prob. 1TYSCh. 11 - Prob. 2TYSCh. 11 - Prob. 3TYSCh. 11 - Prob. 4TYSCh. 11 - Prob. 5TYSCh. 11 - Prob. 6TYSCh. 11 - Prob. 7TYSCh. 11 - Prob. 8TYSCh. 11 - Prob. 9TYSCh. 11 - Prob. 10TYSCh. 11 - Prob. 11TYSCh. 11 - A lamb that weighs 10 pounds at birth gains weight...Ch. 11 - Prob. 13TYS
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- Determining a Solution In Exercises 15-22, determine whether the function is a solution of the differential equation y(4) 16y = 0. 21. y = ln x + ²x + Cx4 -arrow_forwardHow many linearly independent functions are contained in a fundamental set of solutions for the homogeneous differential equation y" + 4y = 0? A fundamental set of solutions of the differential equation contains Choose one Choose one one linearly independent function. two linearly independent functions. three linearly independent functions.arrow_forwardConsider the differential equation da æ(7 – 6t)et dt x + 6 (a) Identify and state the dependent and the independent variables of the differential equation. (b) Classify the above differential equation as directly integrable, separable, or linear differential equation. (c) Find the general solution of the differential equation.arrow_forward
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