Deck 6: Series Solutions of Linear Equations

Question 1

The recurrence relation for the power series solution about of the differential equation is

A)
B)
C)
D)
E)

Answer 1

A

Question 2

A power series solution about of the differential equation is

A)
B)
C)
D)
E)

Answer 2

A

Question 3

For the equation , the point is

A) an ordinary point
B) a regular singular point
C) an irregular singular point
D) a special point
E) none of the above

Answer 3

C

Question 4

The solution of the previous problem is

A)
B)
C)
D)
E)

Question 5

The interval of convergence of the power series in the previous problem is

A)
B)
C)
D)
E)

Question 6

Consider the differential equation . The indicial equation is . The recurrence relation is . A series solution corresponding to the indicial root is

A)
B)
C)
D)
E)

Question 7

In the previous problem, a second solution is

A)
B)
C)
D)
E) none of the above

Question 8

For the equation , the point is

A) an ordinary point
B) a regular singular point
C) an irregular singular point
D) a special point
E) none of the above

Question 9

The differential equation is is

A) Bessel's equation of order 12
B) Bessel's equation of order 3
C) Legendre's equation of order 12
D) Legendre's equation of order 3
E) Legendre's equation of order 4

Question 10

For the equation , the point is

A) an ordinary point
B) a regular singular point
C) an irregular singular point
D) a special point
E) none of the above

Question 11

Find three positive values of for which the differential equation has polynomial solutions.

A) 2, 6, 12
B) 1, 2, 3
C) 1, 4, 9
D) 2, 4, 6
E) 2, 6, 10

Question 12

The solution of the recurrence relation in the previous problem is

A)
B)
C)
D)
E)

Question 13

The solution of the previous problem is

A)
B) , where is given by an infinite series
C)
D)
E)

Question 14

The singular points of the differential equation are

A) none
B) 0
C) 0,
D) 0, 4
E) 0, , 4

Question 15

The recurrence relation for the differential equation is

A)
B)
C)
D)
E)

Question 16

The radius of convergence of the power series is

A) 0
B) 1
C) 2
D)
E) none of the above

Question 17

The first four nonzero terms in the power series expansion of the function about are

A)
B)
C)
D)
E)

Question 18

The differential equation is

A) Bessel's equation of order
B) Bessel's equation of order 1/25
C) Bessel's equation of order 1/5
D) Legendre's equation of order 1/25
E) Legendre's equation of order 1/5

Question 19

The radius of convergence of the power series solution of about is

A) 0
B) 1
C) 2
D)
E) none of the above

Question 20

The indicial equation for the differential equation is

A)
B)
C)
D)
E)

Question 21

The differential equation is

A) Bessel's equation of order
B) Bessel's equation of order 1/16
C) Bessel's equation of order 1/4
D) Legendre's equation of order 1/16
E) Legendre's equation of order 1/4

Question 22

The solution of the previous problem is

A)
B)
C)
D)
E)

Question 23

The radius of convergence of the power series is

A) 0
B) 1
C) 2
D)
E) none of the above

Question 24

The singular points of are Select all that apply.

A) 2
B)
C) 0
D) 1
E) none of the above

Question 25

The recurrence relation for the differential equation is

A)
B)
C)
D)
E)

Question 26

Consider the differential equation The indicial equation is . The recurrence relation is . A series solution corresponding to the indicial root is , where

A)
B)
C)
D)
E)

Question 27

The interval of convergence of the power series in the previous problem is

A)
B)
C)
D)
E)

Question 28

The singular points of the differential equation are

A) none
B) 0
C) 0, 2
D) 0, 3
E) 0, 2, 3

Question 29

For the differential equation , the point is

A) an ordinary point
B) a regular singular point
C) an irregular singular point
D) a special point
E) none of the above

Question 30

The recurrence relation for the power series solution about of the differential equation is (for )

A)
B)
C)
D)
E)

Question 31

In the previous problem, a series solution corresponding to the indicial root is , where

A)
B)
C)
D)
E)

Question 32

The radius of convergence of the power series solution of about is

A) 0
B) 1
C) 2
D)
E) none of the above

Question 33

The indicial equation for the differential equation is

A)
B)
C)
D)
E)

Question 34

A power series solution about of the differential equation is

A)
B)
C)
D)
E)

Question 35

The solution of the previous problem is

A)
B) , where is given by an infinite series
C)
D)
E)

Question 36

For the differential equation , the point is

A) an ordinary point
B) a regular singular point
C) an irregular singular point
D) a special point
E) none of the above

Question 37

For the differential equation , the point is

A) an ordinary point
B) a regular singular point
C) an irregular singular point
D) a special point
E) none of the above

Question 38

The first four terms in the power series expansion of the function about are

A)
B)
C)
D)
E)

Question 39

The solution of the recurrence relation in the previous problem is

A)
B)
C)
D)
E)

Question 40

The differential equation is is

A) Bessel's equation of order 20
B) Bessel's equation of order 4
C) Legendre's equation of order n
D) Legendre's equation of order 20
E) Legendre's equation of order 4