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16.1 Exact First-Order Equations
999
16.1 Exact First-Order Equations
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1.
Find the general solution of the differential equation
.
a.
b.
c.
d.
e.
____
2.
Find the general solution of the differential equation
.
a.
b.
c.
d.
e.
____
3.
Find the general solution of the differential equation
.
a.
b.
c.
d.
e.
1000 Chapter 16: Additional Topics in Differential Equations
____ 4. Find the particular solution of the differential equation
that satisfies the initial condition .
a.
b.
c.
d.
e.
____ 5. Find the particular solution of the differential equation
that satisfies the initial condition .
a.
b.
c.
d.
e.
____ 6.
Find the particular solution of the differential equation
that satisfies the initial condition
.
a.
b.
c.
d.
e.
16.1 Exact First-Order Equations
1001
____ 7.
Find the particular solution of the differential equation
that satisfies the initial condition
.
a.
b.
c.
d.
e.
____ 8. Find the integrating factor of the differential equation that is a function of x or y alone.
a.
b.
c.
d.
e.
____ 9. Find the integrating factor of the differential equation that is a function of x or y alone.
a.
b.
c.
d.
e.
1002 Chapter 16: Additional Topics in Differential Equations
____ 10. Find the integrating factor of the differential equation
that is a function of x or y alone.
a.
b.
c.
d.
e.
____ 11.
Use
as a integrating factor to find the general solution of the
differential equation
.
a.
b.
c.
d.
e.
____ 12. Find an equation for the curve with the slope passing through the
point .
a.
b.
c.
d.
e.
16.1 Exact First-Order Equations
1003
____ 13.
If
represents the cost of producing x units in a manufacturing process, the
elasticity of cost is defined as
. Find the cost function if the
elasticity function is
, where
.
a.
b.
c.
d.
e.
____ 14. Find the value of k such that the differential equation is
exact.
a.
b.
c.
d.
e.
1004
Chapter 16: Additional Topics in Differential Equations
____
15.
Find the general solution of the differential equation
.
a.
b.
c.
d.
e.
16.1 Exact First-Order Equations
1005
Chapter 16 - Section 1
Answer Section
1006 Chapter 16: Additional Topics in Differential Equations
16.2 Second-Order Homogeneous Linear Equations
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Find the general solution of the linear differential equation .
a.
b.
c.
d.
e.
____ 2. Find the general solution of the linear differential equation .
a.
b.
c.
d.
e.
____ 3. Find the general solution of the linear differential equation .
a.
b.
c.
d.
e.
16.2 Second-Order Homogenous Linear Equations
1007
____ 4.
Find the general solution of the linear differential equation
.
a.
b.
c.
d.
e.
____ 5. Find the general solution of the linear differential equation .
a.
b.
c.
d.
e.
____ 6. Find the general solution of the linear differential equation .
a.
b.
c.
d.
e.
____ 7. Find the general solution of the linear differential equation
.
a.
b.
c.
d.
e.
1008
Chapter 16: Additional Topics in Differential Equations
____
8.
Consider the differential equation
and the solution
. Find the particular solution satisfying the initial conditions
.
a.
b.
c.
d.
e.
____
9.
Find the particular solution of the linear differential equation
that
satisfies the initial conditions
.
a.
b.
c.
d.
e.
____ 10.
Find the particular solution of the linear differential equation
that
satisfies the initial conditions
.
a.
b.
c.
d.
e.
16.2 Second-Order Homogenous Linear Equations
1009
____ 11.
Find the particular solution of the linear differential equation
that
satisfies the boundary conditions
, if possible.
a.
b.
c.
d.
e. no solution
____ 12.
Find the particular solution of the linear differential equation
that
satisfies the boundary conditions
, if possible.
a. no solution
b.
c.
d.
e.
____ 13. Suppose a 32-pound weight is suspended on a spring. The weight is pulled foot
below the equilibrium position and released. Assume that the weight stretches the spring foot from
its natural position. Find a formula for the position of the weight as a function of time t.
a.
b.
c.
d.
e.
1010
Chapter 16: Additional Topics in Differential Equations
____
14.
Suppose a 32-pound weight is suspended on a spring. The weight is raised
foot
above the equilibrium position and started off with a downward velocity of foot per second.
Assume that the weight stretches the spring foot from its natural position. Find a formula for the
position of the weight as a function of time t.
a.
b.
c.
d.
e.
16.2 Second-Order Homogenous Linear Equations
1011
____ 15.
Suppose a 32-pound weight is suspended on a spring. The weight is pulled
foot
below the equilibrium position and released. The motion takes place in a Med that furnishes a
damping force of magnitude
speed at all times. Assume that the weight stretches the spring
foot
from its natural position. Find a formula for the position of the weight as a function of time
t. a.
b.
c.
d.
e.
1012
Chapter 16: Additional Topics in Differential Equations
____
16.
Sketch a graph of the solution of the differential equation
with the
initial condition
.
a.
d.
b. e.
c.
16.2 Second-Order Homogenous Linear Equations
1013
16.2 Second-Order Homogeneous Linear Equations
Answer Section
1014 Chapter 16: Additional Topics in Differential Equations
16.3 Second-Order Nonhomogeneous Linear Equations
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Find a particular solution of the differential equation .
a.
b.
c.
d.
e.
____ 2. Find a particular solution of the differential equation .
a.
b.
c.
d.
e.
16.3 Second-Order Nonhomogeneous Linear Equations
1015
____ 3.
Find a particular solution of the differential equation
.
a.
b.
c.
d.
e.
____
4.
Find a particular solution of the differential equation
.
a.
b.
c.
d.
e.
____
5.
Solve the differential equation
by the method of undetermined
coefficients.
a.
b.
c.
d.
e.
