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Zill - Diff. Equations with Modeling 12/e (Metric) (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : – / 28

Due : Sunday, January 27, 2030 00:00 EST

Last Saved : n/a Saving...  ()

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  • Instructions

    A First Course in Differential Equations with Modeling Applications (Metric Version), 12th edition, by Dennis G. Zill, published by Cengage Learning, balances analytical, qualitative, and quantitative approaches to differential equation studies.

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1. –/1 points ZillDiffEQModAp12M 2.2.004. My Notes
Question Part
Points
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1
–/1
0/100
Total
–/1
 
  • This exercise will build problem-solving skills.
  • Read It links are available as a learning tool under each question so students can quickly jump to the corresponding section of the eTextbook.
Solve the given differential equation by separation of variables.
dy − (y − 5)2 dx = 0
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2. –/3 points ZillDiffEQModAp12M 2.3.008.MI. My Notes
Question Part
Points
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1 2 3
–/1 –/1 –/1
0/100 0/100 0/100
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–/3
 
  • This exercise will build problem-solving skills.
  • Students get just-in-time learning support with Watch It videos that contain narrated and closed-captioned videos walking students through the proper steps to solve a similar problem.
Find the general solution of the given differential equation.
y′ = 4y + x2 + 9
y(x) =
Give the largest interval I over which the general solution is defined. (Think about the implications of any singular points. Enter your answer using interval notation.)
Determine whether there are any transient terms in the general solution. (Enter the transient terms as a comma-separated list; if there are none, enter NONE.)

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3. –/14 points ZillDiffEQModAp12M 4.3.037.MI.SA. My Notes
Question Part
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0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100
Total
–/14
 
  • This exercise will build problem-solving skills.
  • Master It tutorials—Standalone are embedded, step-by-step tutorials used to help students understand each step required to solve the problem, before inputting their final answer.
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.

Tutorial Exercise
Solve the given initial-value problem.
y‴ + 12y″ + 36y′ = 0,  y(0) = 0, y′(0) = 1, y″(0) = −5
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4. –/2 points ZillDiffEQModAp12M 4.1.021.EP. My Notes
Question Part
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1 2
–/1 –/1
0/100 0/100
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–/2
 
  • This exercise will develop conceptual understanding.
  • Expanded Problems enhance student understanding by going beyond a basic exercise and asking students to solve each step of the problem in addition to their final answer.
Consider the following functions.
f1(x) = 6 + x,   f2(x) = x,   f3(x) = x2
g(x) = c1f1(x) + c2f2(x) + c3f3(x)
Solve for
c1, c2,
 and
c3
 so that
g(x) = 0
 on the interval
(−∞, ∞).
 If a nontrivial solution exists, state it. (If only the trivial solution exists, enter the trivial solution {0, 0, 0}.)
{c1, c2, c3} = 
Determine whether
f1, f2, and f3
 are linearly independent on the interval
(−∞, ∞).
    
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5. –/2 points ZillDiffEQModAp12M 3.3.007. My Notes
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–/1 –/1
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–/2
 
  • This exercise will develop conceptual understanding.
Consider the two tanks A and B shown in the figure below.
Two cylindrical tanks are shown with 4 pipes connecting them in a system. The first tank is labeled A. The second tank is labeled B.
  • The first pipe connects the top of tank A to a point outside of the image, with an arrow pointing toward tank A that is labeled pure water 3 L/min.
  • The second pipe connects tank A and B on the bottom of the tanks and has an arrow pointing from tank A to tank B labeled mixture 4 L/min.
  • The third pipe connects tank A and B on the top of the tanks and has an arrow pointing from tank B to tank A and is labeled mixture 1 L/min.
  • The fourth pipe connects the bottom of tank B to a point outside of the image, with an arrow pointing away from tank B that is labeled mixture 3 L/min.
Assume that tank A contains 50 liters of water in which 25 kilograms of salt is dissolved. Suppose tank B contains 50 liters of pure water. Liquid is pumped into and out of the tanks as indicated in the figure; the mixture exchanged between the two tanks and the liquid pumped out of tank B are assumed to be well stirred. We wish to construct a mathematical model that describes the number of kilograms
x1(t)
 and
x2(t)
 of salt in tanks A and B, respectively, at time t.
This system is described by the system of equations
dx1
dt
 =  − 
2
25
x1		 + 
1
50
x2
 
dx2
dt
 = 
2
25
x1		 − 
2
25
x2
with initial conditions
x1(0) = 25,
x2(0) = 0.
 What is the system of differential equations if, instead of pure water, a brine solution containing 4 kilograms of salt per liter is pumped into tank A?
dx1
dt
 = 
 
dx2
dt
 = 
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6. –/3 points ZillDiffEQModAp12M 5.1.025.MI. My Notes
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  • This exercise will develop conceptual understanding.
A mass weighing 1.225 N is attached to a spring whose constant is 2 N/m. The medium offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1 m above the equilibrium position with a downward velocity of 12 m/s. Determine the time (in s) at which the mass passes through the equilibrium position. (Use
g = 9.8 m/s2
 for the acceleration due to gravity.)
s
Find the time (in s) after the mass passes through the equilibrium position at which the mass attains its extreme displacement from the equilibrium position.
s
What is the position (in m) of the mass at this instant?
m

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7. –/2 points ZillDiffEQModAp12M 6.1.003. My Notes
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–/2
 
  • This exercise will address readiness gaps.
Find the interval I and radius of convergence R for the given power series. (Enter your answer for interval of convergence using interval notation.)
∞
4n
n
xn
n = 1
I = 
R = 
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8. –/1 points ZillDiffEQModAp12M CR.9.005.MI. My Notes
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  • This exercise will address readiness gaps.

Evaluate the indefinite integral. (Use C for the constant of integration.)
(ln(x))48
x
 dx

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