16.3 Second-Order Nonhomogeneous Linear Equations 985
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.
986 Chapter 16: Additional Topics in Differential Equations
____ 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.
16.3 Second-Order Nonhomogeneous Linear Equations 987
____ 6. Solve the differential equation by the method of undetermined
coefficients.
a.
b.
c.
d.
e.
____ 7. Solve the differential equation by the method of
undetermined coefficients.
a.
b.
c.
d.
e.
988 Chapter 16: Additional Topics in Differential Equations
____ 8. Solve the differential equation by the method of undetermined
coefficients.
a.
b.
c.
d.
e.
____ 9. Solve the differential equation , where by the
method of undetermined coefficients.
a.
b.
c.
d.
e.
____ 10. Solve the differential equation , where
by the method of undetermined coefficients.
a.
b.
c.
d.
e.
16.3 Second-Order Nonhomogeneous Linear Equations 989
____ 11. Solve the differential equation by the method of variation of
parameters.
a.
b.
c.
d.
e.
____ 12. Solve the differential equation by the method of variation of
parameters.
a.
b.
c.
d.
e.
____ 13. Using the method of undetermined coefficients, determine the most suitable choice
for given . (You do not need to solve the differential equation.)
a.
b.
c.
d.
e.
990 Chapter 16: Additional Topics in Differential Equations
____ 14. Use the electrical circuit differential equation
where is the resistance (in ohms), is the capacitance (in farads), is the
inductance (in henrys), is the electromotive force (in volts), and q is the charge on the
capacitor (in coulombs). Find the charge q as a function of time for the electrical circuit described.
Assume that and .
a.
b.
c.
d.
e.
____ 15. Find the particular solution of the differential equation
for the oscillating motion of an object on the end of a spring. In the
equation, y is the displacement from equilibrium (positive direction is downward) measured in feet,
and t is the time in seconds (see figure). The constant is the weight of the object, is the
acceleration due to gravity, is the magnitude of the resistance to the motion, is the spring
constant from Hooke’s Law, is the acceleration imposed on the system, and
.
a.
16.3 Second-Order Nonhomogeneous Linear Equations 991
b.
c.
d.
e.
____ 16. Find the particular solution of the differential equation
for the oscillating motion of an object on the end of a spring. In the
equation, y is the displacement from equilibrium (positive direction is downward) measured in feet,
and t is the time in seconds (see figure). The constant is the weight of the object, is the
acceleration due to gravity, is the magnitude of the resistance to the motion, is the spring
constant from Hooke’s Law, is the acceleration imposed on the system, and
.
a.
b.
c.
d.
e.
992 Chapter 16: Additional Topics in Differential Equations
____ 17. Find the particular solution of the differential equation
for the oscillating motion of an object on the end of a spring. In the
equation, y is the displacement from equilibrium (positive direction is downward) measured in feet,
and t is the time in seconds (see figure). The constant is the weight of the object, is the
acceleration due to gravity, is the magnitude of the resistance to the motion, is the
spring constant from Hooke’s Law, is the acceleration imposed on the system,
and .
a.
b.
c.
d.
e.
16.3 Second-Order Nonhomogeneous Linear Equations 993
____ 18. Solve the differential equation given that and
are solutions of the corresponding homogeneous equation.
a.
b.
c.
d.
e.
994 Chapter 16: Additional Topics in Differential Equations
16.3 Second-Order Nonhomogeneous Linear Equations – Answer Section