Multivariable Calculus - With WebAssign
11th Edition
ISBN: 9781337604796
Author: Larson
Publisher: CENGAGE L
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Chapter 16.3, Problem 11E
To determine
To calculate: The solution of the given differential equation
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test for homogeneity and solve the differential equation
Solve the differential equation
a) State the order of the differential equation and determine whether the equation is linear or
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(x-)+ +-
7t = 0
Chapter 16 Solutions
Multivariable Calculus - With WebAssign
Ch. 16.1 - Exactness What does it mean for the...Ch. 16.1 - Integrating Factor When is it beneficial to use an...Ch. 16.1 - Testing for Exactness In Exercises 3-6, determine...Ch. 16.1 - Testing for Exactness In Exercises 3-6, determine...Ch. 16.1 - Prob. 5ECh. 16.1 - Prob. 6ECh. 16.1 - Prob. 7ECh. 16.1 - Solving an Exact Differential Equation In...Ch. 16.1 - Prob. 9ECh. 16.1 - Prob. 10E
Ch. 16.1 - Prob. 11ECh. 16.1 - Prob. 12ECh. 16.1 - Prob. 13ECh. 16.1 - Prob. 14ECh. 16.1 - Prob. 15ECh. 16.1 - Graphical and Analytic AnalysisIn Exercises 15 and...Ch. 16.1 - Prob. 17ECh. 16.1 - Prob. 18ECh. 16.1 - Prob. 19ECh. 16.1 - Finding a Particular SolutionIn Exercises 17-22,...Ch. 16.1 - Prob. 21ECh. 16.1 - Prob. 22ECh. 16.1 - Prob. 23ECh. 16.1 - Prob. 24ECh. 16.1 - Prob. 25ECh. 16.1 - Prob. 26ECh. 16.1 - Prob. 27ECh. 16.1 - Finding an Integrating Factor In Exercises 23-32,...Ch. 16.1 - Prob. 29ECh. 16.1 - Prob. 30ECh. 16.1 - Prob. 31ECh. 16.1 - Prob. 32ECh. 16.1 - Prob. 33ECh. 16.1 - Using an Integrating Factor In Exercises 33-36,...Ch. 16.1 - Prob. 35ECh. 16.1 - Prob. 36ECh. 16.1 - Prob. 37ECh. 16.1 - Prob. 38ECh. 16.1 - Tangent Curves In Exercises 39-42, use agraphing...Ch. 16.1 - Prob. 40ECh. 16.1 - Prob. 41ECh. 16.1 - Prob. 42ECh. 16.1 - Prob. 43ECh. 16.1 - Finding an Equation of a Curve In Exercises 43 and...Ch. 16.1 - Cost In a manufacturing process where y=C(x)...Ch. 16.1 - HOW DO YOU SEE? The graph shows several...Ch. 16.1 - Prob. 47ECh. 16.1 - Prob. 48ECh. 16.1 - Prob. 49ECh. 16.1 - Prob. 50ECh. 16.1 - Prob. 51ECh. 16.1 - Prob. 52ECh. 16.1 - Prob. 53ECh. 16.1 - Prob. 54ECh. 16.1 - Prob. 55ECh. 16.1 - Prob. 56ECh. 16.1 - Prob. 57ECh. 16.1 - Prob. 58ECh. 16.2 - Prob. 1ECh. 16.2 - Prob. 2ECh. 16.2 - Prob. 3ECh. 16.2 - Prob. 4ECh. 16.2 - Prob. 5ECh. 16.2 - Prob. 6ECh. 16.2 - Prob. 7ECh. 16.2 - Prob. 8ECh. 16.2 - Prob. 9ECh. 16.2 - Prob. 10ECh. 16.2 - Prob. 11ECh. 16.2 - Prob. 12ECh. 16.2 - Prob. 13ECh. 16.2 - Prob. 14ECh. 16.2 - Prob. 15ECh. 16.2 - Prob. 16ECh. 16.2 - Prob. 17ECh. 16.2 - Prob. 18ECh. 16.2 - Prob. 19ECh. 16.2 - Prob. 20ECh. 16.2 - Prob. 21ECh. 16.2 - Prob. 22ECh. 16.2 - Prob. 23ECh. 16.2 - Prob. 24ECh. 16.2 - Prob. 25ECh. 16.2 - Prob. 26ECh. 16.2 - Prob. 27ECh. 16.2 - Prob. 28ECh. 16.2 - Prob. 29ECh. 16.2 - Prob. 30ECh. 16.2 - Prob. 31ECh. 16.2 - Finding a General Solution In exercises 9-36, find...Ch. 16.2 - Prob. 33ECh. 16.2 - Prob. 34ECh. 16.2 - Prob. 35ECh. 16.2 - Prob. 36ECh. 16.2 - Prob. 37ECh. 16.2 - Finding a Particular Solution Determine C and ...Ch. 16.2 - Prob. 39ECh. 16.2 - Prob. 40ECh. 16.2 - Prob. 41ECh. 16.2 - Find a Particular Solution: Initial ConditionsIn...Ch. 16.2 - Prob. 43ECh. 16.2 - Prob. 44ECh. 16.2 - Prob. 45ECh. 16.2 - Prob. 46ECh. 16.2 - Prob. 47ECh. 16.2 - Finding a Particular Solution: Boundary...Ch. 16.2 - Prob. 49ECh. 16.2 - Prob. 50ECh. 16.2 - Prob. 51ECh. 16.2 - Prob. 52ECh. 16.2 - Several shock absorbers are shown at the right. Do...Ch. 16.2 - Prob. 54ECh. 16.2 - Prob. 55ECh. 16.2 - Prob. 56ECh. 16.2 - Motion of a Spring In Exercise 55-58, match the...Ch. 16.2 - Prob. 58ECh. 16.2 - Prob. 59ECh. 16.2 - Prob. 60ECh. 16.2 - Prob. 61ECh. 16.2 - Prob. 62ECh. 16.2 - Prob. 63ECh. 16.2 - Prob. 64ECh. 16.2 - Prob. 65ECh. 16.2 - Prob. 66ECh. 16.2 - Prob. 67ECh. 16.2 - True or False? In exercises 67-70, determine...Ch. 16.2 - Prob. 69ECh. 16.2 - Prob. 70ECh. 16.2 - Wronskian The Wronskian of two differentiable...Ch. 16.2 - Prob. 72ECh. 16.2 - Prob. 73ECh. 16.2 - Prob. 74ECh. 16.3 - Prob. 1ECh. 16.3 - Choosing a MethodDetermine whether you woulduse...Ch. 16.3 - Prob. 3ECh. 16.3 - Prob. 4ECh. 16.3 - Prob. 5ECh. 16.3 - Prob. 6ECh. 16.3 - Prob. 7ECh. 16.3 - Prob. 8ECh. 16.3 - Prob. 9ECh. 16.3 - Prob. 10ECh. 16.3 - Prob. 11ECh. 16.3 - Prob. 12ECh. 16.3 - Prob. 13ECh. 16.3 - Method of Undetermined CoefficientsIn Exercises...Ch. 16.3 - Prob. 15ECh. 16.3 - Prob. 16ECh. 16.3 - Prob. 17ECh. 16.3 - Prob. 18ECh. 16.3 - Prob. 19ECh. 16.3 - Using Initial Conditions In Exercises 17-22, solve...Ch. 16.3 - Prob. 21ECh. 16.3 - Prob. 22ECh. 16.3 - Prob. 23ECh. 16.3 - Prob. 24ECh. 16.3 - Prob. 25ECh. 16.3 - Prob. 26ECh. 16.3 - Prob. 27ECh. 16.3 - Method of Variation of Parameters In Exercises...Ch. 16.3 - Prob. 29ECh. 16.3 - Electrical Circuits In Exercises 29 and 30, use...Ch. 16.3 - Prob. 31ECh. 16.3 - Prob. 32ECh. 16.3 - Prob. 33ECh. 16.3 - Prob. 34ECh. 16.3 - Prob. 35ECh. 16.3 - Prob. 36ECh. 16.3 - Prob. 37ECh. 16.3 - Prob. 38ECh. 16.3 - Prob. 39ECh. 16.3 - Prob. 40ECh. 16.3 - Prob. 41ECh. 16.4 - Prob. 1ECh. 16.4 - Prob. 2ECh. 16.4 - Prob. 3ECh. 16.4 - Power Series Solution In Exercises 3-6, use a...Ch. 16.4 - Prob. 5ECh. 16.4 - Prob. 6ECh. 16.4 - Prob. 7ECh. 16.4 - Prob. 8ECh. 16.4 - Prob. 9ECh. 16.4 - Prob. 10ECh. 16.4 - Prob. 11ECh. 16.4 - Prob. 12ECh. 16.4 - Prob. 13ECh. 16.4 - Prob. 14ECh. 16.4 - Prob. 15ECh. 16.4 - Prob. 16ECh. 16.4 - Prob. 17ECh. 16.4 - Prob. 18ECh. 16.4 - Prob. 19ECh. 16.4 - Prob. 20ECh. 16.4 - Prob. 21ECh. 16.4 - Prob. 22ECh. 16.4 - Prob. 23ECh. 16.4 - Prob. 24ECh. 16.4 - Airys Equation Find the first six terms of the...Ch. 16 - Prob. 1RECh. 16 - Prob. 2RECh. 16 - Prob. 3RECh. 16 - Prob. 4RECh. 16 - Prob. 5RECh. 16 - Solving an Exact Differential Equation In...Ch. 16 - Prob. 7RECh. 16 - Prob. 8RECh. 16 - Prob. 9RECh. 16 - Prob. 10RECh. 16 - Prob. 11RECh. 16 - Prob. 12RECh. 16 - Prob. 13RECh. 16 - Prob. 14RECh. 16 - Prob. 15RECh. 16 - Prob. 16RECh. 16 - Prob. 17RECh. 16 - Prob. 18RECh. 16 - Prob. 19RECh. 16 - Prob. 20RECh. 16 - Prob. 21RECh. 16 - Prob. 22RECh. 16 - Prob. 23RECh. 16 - Prob. 24RECh. 16 - Prob. 25RECh. 16 - Prob. 26RECh. 16 - Prob. 27RECh. 16 - Prob. 28RECh. 16 - Prob. 29RECh. 16 - Prob. 30RECh. 16 - Prob. 31RECh. 16 - Prob. 32RECh. 16 - Prob. 33RECh. 16 - Prob. 34RECh. 16 - Prob. 35RECh. 16 - Motion of a SpringIn Exercise 35-36, a 64-pound...Ch. 16 - Prob. 37RECh. 16 - Prob. 38RECh. 16 - Prob. 39RECh. 16 - Prob. 40RECh. 16 - Prob. 41RECh. 16 - Prob. 42RECh. 16 - Prob. 43RECh. 16 - Prob. 44RECh. 16 - Prob. 45RECh. 16 - Using Initial Conditions In Exercises 45-50, solve...Ch. 16 - Prob. 47RECh. 16 - Prob. 48RECh. 16 - Prob. 49RECh. 16 - Prob. 50RECh. 16 - Method of Variation of Parameters In Exercises...Ch. 16 - Prob. 52RECh. 16 - Prob. 53RECh. 16 - Prob. 54RECh. 16 - Prob. 55RECh. 16 - Prob. 56RECh. 16 - Prob. 57RECh. 16 - Prob. 58RECh. 16 - Prob. 59RECh. 16 - Prob. 60RECh. 16 - Prob. 61RECh. 16 - Prob. 62RECh. 16 - Prob. 1PSCh. 16 - Prob. 2PSCh. 16 - Prob. 3PSCh. 16 - Prob. 4PSCh. 16 - Prob. 5PSCh. 16 - Prob. 6PSCh. 16 - Prob. 7PSCh. 16 - Prob. 8PSCh. 16 - Pendulum Consider a pendulum of length L that...Ch. 16 - Prob. 10PSCh. 16 - Prob. 11PSCh. 16 - Prob. 12PSCh. 16 - Prob. 13PSCh. 16 - Prob. 14PSCh. 16 - Prob. 15PSCh. 16 - ChebyshevsEquation ConsiderChebyshevs equation...Ch. 16 - Prob. 17PSCh. 16 - Prob. 18PSCh. 16 - Prob. 19PSCh. 16 - Laguerres Equation Consider Laguerres Equation...
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- Van der Waals Equation In Exercise 18 at the end of Section 2.3, we discussed the ideal gas law, which shows the relationship among volume V, pressure p, and temperature T for a fixed amount 1 mole of a gas. But chemists believe that in many situations, the van der Waals equation gives more accurate results. If we measure temperature T in kelvins, volume V in liters, and pressure p in atmosphere 1 atm is the pressure exerted by the atmosphere at sea level, then the relationship for carbon dioxide is given by p=0.082TV0.0433.592V2atm What volume does this equation predict for 1 mole of carbon dioxide at 500 kelvins and 100 atm?Suggestion: Consider volumes ranging from 0.1 to 1 liter.arrow_forwardSOLVE THE DIFFERENTIAL EQUATION USING PROPER METHOD DIFFERETIATE WHAT METHOD USEDarrow_forwardTutorial Exercise Consider the differential equation x²y" - 4xy' + 6y=0; x², x³², (0, on). Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval. Form the general solution. Step 1 We are given the following homogenous differential equation and pair of solutions on the given interval. x²y" - 4xy + 6y=0; x², x³, (0, 0) We are asked to verify that the solutions are linearly independent. That is, there do not exist constants c, and c₂, not both zero, s are different powers of x, we have a formal test to verify the linear independence. Recall the definition of the Wronskian for the case of two functions f, and f, each of which have a first derivative. f₂ W(f₁, f₂) = Will HOUTBEave any pronTIES FOR LA By Theorem 4.1.3, if W(f₁, f₂) 0 for every x in the interval of the solution, then solutions are linearly independent. Let f(x) = x² and f(x) = x³. Complete the Wronskian for these functions. x² w(x², x³) = 2xarrow_forward
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