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16.4 Series Solutions of Differential Equations 995
16.4 Series Solutions of Differential Equations
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Use a power series to solve the differential equation .
a. , where is an arbitrary constant
b. , where is an arbitrary constant
c. , where is an arbitrary constant
d. , where is an arbitrary constant
e. , where is an arbitrary constant
____ 2. Use a power series to solve the differential equation .
a. , where and are arbitrary constants
b. , where and are arbitrary constants
c. , where and are arbitrary constants
d. , where and are arbitrary constants
e. , where and are arbitrary constants
____ 3. Use a power series to solve the differential equation .
a. , where and are arbitrary constants
b. , where and are arbitrary constants
c. , where and are arbitrary constants
d. , where and are arbitrary constants
e. , where and are arbitrary constants
____ 4. Solve the differential equation .
a.
, where is an arbitrary constant
b.
, where is an arbitrary constant
996 Chapter 16: Additional Topics in Differential Equations
c.
, where is an arbitrary constant
d.
, where is an arbitrary constant
e.
, where is an arbitrary constant
____ 5. Find the interval of convergence for the solution of the differential equation
.
a.
b.
c.
d.
e.
____ 6. Solve the differential equation .
a.
, where and are arbitrary constants
b.
, where and are arbitrary constants
c.
, where and are arbitrary constants
d.
, where and are arbitrary constants
e.
, where and are arbitrary constants
16.4 Series Solutions of Differential Equations 997
____ 7. Find the interval of convergence for the solution of the differential equation
.
a.
b.
c.
d.
e.
____ 8. Solve the differential equation .
a.
, where is an arbitrary constant
b.
, where and are arbitrary constants
c.
, where and are arbitrary
constants
d.
, where and are arbitrary
constants
e.
, where and are arbitrary constants
____ 9. Find the interval of convergence for the solution of the differential equation
.
a.
b.
c.
d.
e.
998 Chapter 16: Additional Topics in Differential Equations
____ 10. Find the first six terms of the power series representing independent solutions of the
differential equation .
a.
, where and are arbitrary
constants
b.
, where and are arbitrary
constants
c.
, where and are arbitrary
constants
d.
, where and are arbitrary
constants
e.
, where and are arbitrary
constants
____ 11. Find the first eight terms of the power series representing independent solutions of
the differential equation .
a.
, where and are
arbitrary constants
16.4 Series Solutions of Differential Equations 999
b.
where and are arbitrary constants
c.
,
where and are arbitrary constants
d.
, where and are
arbitrary constants
e.
,
where and are arbitrary constants
____ 12. Use Taylor's Theorem to find the first five terms of the series solution of
given the initial condition .
a.
b.
c.
d.
e.
1000 Chapter 16: Additional Topics in Differential Equations
____ 13. Use Taylor's Theorem to find the first four terms of the series solution of
given the initial condition and use it to calculate . Round your answer to three decimal
places wherever applicable.
a.
b.
c.
d.
e.
____ 14. Find the series solution of the differential equation given the initial
conditions and .
a.
b.
c.
d.
e.
16.4 Series Solutions of Differential Equations 1001
____ 15. Use Taylor's Theorem to find the first six terms of the series solution of
given the initial conditions and .
a.
b.
c.
d.
e.
____ 16. Use Taylor's Theorem to find the first eight terms of the series solution of
given the initial conditions and use it to calculate . Round
your answer to three decimal places.
a.
b.
c.
d.
e.
1002 Chapter 16: Additional Topics in Differential Equations
____ 17. Use Taylor's Theorem to find the first four terms of the series solution of
given the initial conditions .
a.
b.
c.
d.
e.
____ 18. Use Taylor's Theorem to find the first four terms of the series solution of
given the initial conditions and use it to calculate
. Round your answer to three decimal places.
a.
b.
c.
d.
e.
16.4 Series Solutions of Differential Equations 1003
16.4 Series Solutions of Differential Equations – Answer Section
