Fundamentals of Differential Equations and Boundary Value Problems
7th Edition
ISBN: 9780321977106
Author: Nagle, R. Kent
Publisher: Pearson Education, Limited
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Chapter 2.6, Problem 40E
To determine
To solve:
The given differential equation
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Can you show me a step by step explanation please.
2. A tank with a capacity of 650 gal. originally contains 200 gal of water with 100 lb. of salt in
solution. Water containing 1 lb. of salt per gallon is entering at a rate of 4 gal/min, and the
mixture is allowed to flow out of the tank at a rate of 3 gal/min.
a. Find the amount of salt in the tank at any time prior to the instant when the tank
begins to overflow (650 gallons).
b. Find the concentration (in pounds per gallon) of salt in the tank when the tank hits
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D.E. for mixture problems:
dv
dt=11-12
dA
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dy
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a. What are the equilibrium solutions for the differential equation?
b. Where is the differential equation increasing or decreasing? Show how you know.
Showing them on the drawing is not enough.
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d. Consider the slope field for the differential equation. Draw solution curves given the
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i. y(0) = -5
ii. y(0) = -1
iii. y(0) = 2
Chapter 2 Solutions
Fundamentals of Differential Equations and Boundary Value Problems
Ch. 2.2 - Prob. 1ECh. 2.2 - In Problems 1-6, determine whether the given...Ch. 2.2 - Prob. 3ECh. 2.2 - Prob. 4ECh. 2.2 - Prob. 5ECh. 2.2 - Prob. 6ECh. 2.2 - Prob. 7ECh. 2.2 - Prob. 8ECh. 2.2 - Prob. 9ECh. 2.2 - Prob. 10E
Ch. 2.2 - Prob. 11ECh. 2.2 - Prob. 12ECh. 2.2 - Prob. 13ECh. 2.2 - Prob. 14ECh. 2.2 - Prob. 15ECh. 2.2 - Prob. 16ECh. 2.2 - Prob. 17ECh. 2.2 - Prob. 18ECh. 2.2 - Prob. 19ECh. 2.2 - Prob. 20ECh. 2.2 - Prob. 21ECh. 2.2 - Prob. 22ECh. 2.2 - Prob. 23ECh. 2.2 - Prob. 24ECh. 2.2 - Prob. 25ECh. 2.2 - Prob. 26ECh. 2.2 - Solutions Not Expressible in Terms of Elementary...Ch. 2.2 - Sketch the solution to the initial value problem...Ch. 2.2 - Prob. 29ECh. 2.2 - As stated in this section, the separation of...Ch. 2.2 - Interval of Definition. By looking at an initial...Ch. 2.2 - Analyze the solution y=(x) to the initial value...Ch. 2.2 - Prob. 33ECh. 2.2 - Prob. 34ECh. 2.2 - Prob. 35ECh. 2.2 - Prob. 36ECh. 2.2 - Prob. 37ECh. 2.2 - Prob. 38ECh. 2.2 - Prob. 39ECh. 2.2 - The atmospheric pressure force per unit area on a...Ch. 2.3 - In Problem 1-6, Determine whether the given...Ch. 2.3 - Prob. 2ECh. 2.3 - Prob. 3ECh. 2.3 - Prob. 4ECh. 2.3 - Prob. 5ECh. 2.3 - Prob. 6ECh. 2.3 - Prob. 7ECh. 2.3 - In Problems 7-16, obtain the general solution to...Ch. 2.3 - In Problems 7-16, obtain the general solution to...Ch. 2.3 - Prob. 10ECh. 2.3 - In Problems 7-16, obtain the general solution to...Ch. 2.3 - Prob. 12ECh. 2.3 - Prob. 13ECh. 2.3 - In Problems 7-16, obtain the general solution to...Ch. 2.3 - In Problems 7-16, obtain the general solution to...Ch. 2.3 - In Problems 7-16, obtain the general solution to...Ch. 2.3 - In Problems 17-22, solve the initial value...Ch. 2.3 - In Problem 17-22, solve the initial value problem....Ch. 2.3 - In Problem 17-22, solve the initial value problem....Ch. 2.3 - Prob. 20ECh. 2.3 - Prob. 21ECh. 2.3 - Prob. 22ECh. 2.3 - Prob. 23ECh. 2.3 - Prob. 24ECh. 2.3 - Prob. 25ECh. 2.3 - Prob. 26ECh. 2.3 - Constant Multiples of Solutions. a. Show that y=ex...Ch. 2.3 - Prob. 29ECh. 2.3 - Prob. 30ECh. 2.3 - Discontinuous Coefficients. As we will see in...Ch. 2.3 - Prob. 32ECh. 2.3 - Prob. 33ECh. 2.3 - Prob. 34ECh. 2.3 - Mixing Suppose a brine containing 0.2kg of salt...Ch. 2.3 - Variation of Parameters. Here is another procedure...Ch. 2.3 - Prob. 37ECh. 2.3 - Prob. 38ECh. 2.3 - The Nobel Prize in Physiology or Medicine in 1963...Ch. 2.4 - Prob. 1ECh. 2.4 - Prob. 2ECh. 2.4 - Prob. 3ECh. 2.4 - Prob. 4ECh. 2.4 - Prob. 5ECh. 2.4 - Prob. 6ECh. 2.4 - Prob. 7ECh. 2.4 - Prob. 8ECh. 2.4 - Prob. 9ECh. 2.4 - Prob. 10ECh. 2.4 - Prob. 11ECh. 2.4 - Prob. 12ECh. 2.4 - Prob. 13ECh. 2.4 - Prob. 14ECh. 2.4 - Prob. 15ECh. 2.4 - Prob. 16ECh. 2.4 - Prob. 17ECh. 2.4 - Prob. 18ECh. 2.4 - Prob. 19ECh. 2.4 - In Problems 9-20, determine whether the equation...Ch. 2.4 - Prob. 21ECh. 2.4 - Prob. 22ECh. 2.4 - Prob. 23ECh. 2.4 - Prob. 24ECh. 2.4 - Prob. 25ECh. 2.4 - Prob. 26ECh. 2.4 - Prob. 27ECh. 2.4 - Prob. 28ECh. 2.4 - Prob. 29ECh. 2.4 - Consider the equation...Ch. 2.4 - Prob. 31ECh. 2.4 - Prob. 32ECh. 2.4 - Prob. 33ECh. 2.4 - Prob. 34ECh. 2.4 - Prob. 35ECh. 2.4 - Prob. 36ECh. 2.5 - Prob. 1ECh. 2.5 - Prob. 2ECh. 2.5 - Prob. 3ECh. 2.5 - Prob. 4ECh. 2.5 - Prob. 5ECh. 2.5 - Prob. 6ECh. 2.5 - In Problems 7-12, solve the equation....Ch. 2.5 - In Problems 7-12, solve the equation....Ch. 2.5 - In Problems 7-12, solve the equation....Ch. 2.5 - In Problems 7-12, solve the equation....Ch. 2.5 - In Problems 7-12, solve the equation....Ch. 2.5 - In Problems 7-12, solve the equation....Ch. 2.5 - Prob. 13ECh. 2.5 - Prob. 14ECh. 2.5 - Prob. 15ECh. 2.5 - Prob. 16ECh. 2.5 - Prob. 17ECh. 2.5 - Prob. 18ECh. 2.5 - Prob. 19ECh. 2.5 - Prob. 20ECh. 2.6 - Prob. 1ECh. 2.6 - Prob. 2ECh. 2.6 - Prob. 3ECh. 2.6 - Prob. 4ECh. 2.6 - In Problems 1 -8, identify do not solve the...Ch. 2.6 - In Problems 1 -8, identify do not solve the...Ch. 2.6 - Prob. 7ECh. 2.6 - In Problems 1 -8, identify do not solve the...Ch. 2.6 - Prob. 9ECh. 2.6 - Use the method discussed under Homogeneous...Ch. 2.6 - Prob. 11ECh. 2.6 - Prob. 12ECh. 2.6 - Prob. 13ECh. 2.6 - Prob. 14ECh. 2.6 - Prob. 15ECh. 2.6 - Prob. 16ECh. 2.6 - Prob. 17ECh. 2.6 - Prob. 18ECh. 2.6 - Prob. 19ECh. 2.6 - Use the method discussed under Equations of the...Ch. 2.6 - Prob. 21ECh. 2.6 - Prob. 22ECh. 2.6 - Prob. 23ECh. 2.6 - Prob. 24ECh. 2.6 - Prob. 25ECh. 2.6 - Prob. 26ECh. 2.6 - Prob. 27ECh. 2.6 - Prob. 28ECh. 2.6 - Prob. 29ECh. 2.6 - Prob. 30ECh. 2.6 - Use the method discussed under Equations with...Ch. 2.6 - Use method discussed under Equation with Linear...Ch. 2.6 - Prob. 33ECh. 2.6 - Prob. 34ECh. 2.6 - Prob. 35ECh. 2.6 - Prob. 36ECh. 2.6 - Prob. 37ECh. 2.6 - Prob. 38ECh. 2.6 - Prob. 39ECh. 2.6 - Prob. 40ECh. 2.6 - Prob. 41ECh. 2.6 - Prob. 42ECh. 2.6 - Prob. 43ECh. 2.6 - Prob. 44ECh. 2.6 - Prob. 45ECh. 2.6 - Prob. 46ECh. 2.6 - Prob. 47ECh. 2.6 - Prob. 48ECh. 2.RP - Prob. 1RPCh. 2.RP - Prob. 2RPCh. 2.RP - Prob. 3RPCh. 2.RP - Prob. 4RPCh. 2.RP - Prob. 5RPCh. 2.RP - Prob. 6RPCh. 2.RP - Prob. 7RPCh. 2.RP - Prob. 8RPCh. 2.RP - Prob. 9RPCh. 2.RP - Prob. 10RPCh. 2.RP - Prob. 11RPCh. 2.RP - Prob. 12RPCh. 2.RP - Prob. 13RPCh. 2.RP - Prob. 14RPCh. 2.RP - Prob. 15RPCh. 2.RP - Prob. 16RPCh. 2.RP - Prob. 17RPCh. 2.RP - Prob. 18RPCh. 2.RP - Prob. 19RPCh. 2.RP - Prob. 20RPCh. 2.RP - Prob. 21RPCh. 2.RP - In Problem 1-30, solve the equation....Ch. 2.RP - Prob. 23RPCh. 2.RP - Prob. 24RPCh. 2.RP - Prob. 25RPCh. 2.RP - Prob. 26RPCh. 2.RP - In Problems 1-30, solve the equation....Ch. 2.RP - Prob. 28RPCh. 2.RP - Prob. 29RPCh. 2.RP - Prob. 30RPCh. 2.RP - Prob. 31RPCh. 2.RP - Prob. 32RPCh. 2.RP - In Problems 31-40, solve the initial value problem...Ch. 2.RP - Prob. 34RPCh. 2.RP - Prob. 35RPCh. 2.RP - Prob. 36RPCh. 2.RP - Prob. 37RPCh. 2.RP - Prob. 38RPCh. 2.RP - Prob. 39RPCh. 2.RP - Prob. 40RPCh. 2.RP - Prob. 41RP
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