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16.2 Second-Order Homogenous Linear Equations 977
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.
978 Chapter 16: Additional Topics in Differential Equations
____ 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.
16.2 Second-Order Homogenous Linear Equations 979
____ 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.
980 Chapter 16: Additional Topics in Differential Equations
____ 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.
16.2 Second-Order Homogenous Linear Equations 981
____ 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.
____ 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.
982 Chapter 16: Additional Topics in Differential Equations
d.
e.
____ 16. Sketch a graph of the solution of the differential equation with the
initial condition .
a. d.
c.
16.2 Second-Order Homogenous Linear Equations 983
b. e.
c.
984 Chapter 16: Additional Topics in Differential Equations
16.2 Second-Order Homogeneous Linear Equations
Answer Section
MULTIPLE CHOICE
