Deck 16: Mathematics Problems: Differential Equations and Linear Algebra

Question 1

The solution of is

A)
B)
C)
D)
E)

Answer 1

C

Question 2

The solution of is

A)
B)
C)
D)
E)

Answer 2

D

Question 3

The solution of

A)
B)
C)
D)
E)

Answer 3

E

Question 4

The correct form of the particular solution of is

A)
B)
C)
D)
E)

Question 5

The solution of is

A)
B)
C)
D)
E)

Question 6

The solution of is

A)
B)
C)
D)
E)

Question 7

The solution of is

A)
B)
C)
D)
E)

Question 8

The solution of is

A)
B)
C)
D)
E)

Question 9

The auxiliary equation of is

A)
B)
C)
D)
E)

Question 10

The solution of is

A)
B)
C)
D)
E)

Question 11

The solution of is

A)
B)
C)
D)
E)

Question 12

The solution of is

A)
B)
C)
D)
E)

Question 13

The correct form of the particular solution of is

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

Question 14

A frozen chicken at is taken out of the freezer and placed on a table at . One hour later the temperature of the chicken is . The mathematical model for the temperature as a function of time is (assuming Newton's law of warming)

A)
B)
C)
D)
E)

Question 15

The solution of is

A)
B)
C)
D)
E)

Question 16

A 2-pound weight is hung on a spring and stretches it 1/2 foot. The mass spring system is then put into motion in a medium offering a damping force numerically equal to the velocity. If the mass is pulled down 4 inches from equilibrium and released, the initial value problem describing the position, , of the mass at time is

A)
B)
C)
D)
E)

Question 17

In the previous problem, the solution of the differential equation is

A)
B)
C)
D)
E)

Question 18

In the previous two problems, the solution for the temperature is

A)
B)
C)
D)
E)

Question 19

In the previous problem, the solution for the position, , is

A)
B)
C)
D)
E)

Question 20

The solution of is

A)
B)
C)
D)
E)

Question 21

Using Laplace transform methods, the solution of is (Hint: the previous problem might be useful.)

A)
B)
C)
D)
E)

Question 22

Let . Then

A)
B)
C)
D)
E)

Question 23

The solution of the previous problem is

A)
B)
C)
D)
E)

Question 24

Using Laplace transform methods, the solution of is

A)
B)
C)
D)
E)

Question 25

In the previous problem, the exact solution of the initial value problem is

A)
B)
C)
D)
E)

Question 26

The eigenvalues of the matrix are

A)
B)
C) 1, 2
D) 2, 3
E) 2, 2

Question 27

The solution of is

A)
B)
C)
D)
E)

Question 28

The solution of is

A)
B)
C)
D)
E)

Question 29

A particular solution of is

A)
B)
C)
D)
E)

Question 30

Using the improved Euler method with a step size of , the solution of at is

A)
B)
C)
D)
E)

Question 31

Using the convolution theorem, we find that

A)
B)
C)
D)
E)

Question 32

The solution of is

A)
B)
C)
D)
E)

Question 33

In the previous two problems, the error in the improved Euler method at is

A) 0.00467
B) 0.000168
C) 0.870
D) 0.895
E) 0.0897

Question 34

Using Laplace transform methods, the solution of is

A)
B)
C)
D)
E)

Question 35

A uniform beam of length 10 has a concentrated load at . It is embedded at both ends. The boundary value problem for the deflections, , for this system is

A)
B)
C)
D)
E)

Question 36

The eigenvalues of the matrix are

A) 1, 2, 3
B) 2, 2, 3
C) 1, 2, 2
D)
E)

Question 37

Using power series methods, the solution of is

A)
B)
C)
D)
E)

Question 38

Using power series methods, the solution of is

A)
B)
C)
D)
E)

Question 39

The solution of the eigenvalue problem is

A)
B)
C)
D)
E)

Question 40

The eigenvalues of the matrix are

A)
B)
C)
D)
E)

Question 41

In the previous problem, the error in the classical Runge-Kutta method at is (Hint: see the previous five problems.)

A) 0.0008
B) 0.00008
C) 0.00000008
D) 0.000008
E) 0.0000008

Question 42

The eigenvalues of the matrix are

A)
B)
C)
D)
E)

Question 43

The differential equation is Select all that apply.

A) linear
B) separable
C) exact
D) non-linear
E) Bernoulli

Question 44

Consider the boundary-value problem . Replace the derivatives with central differences with a step size of . The resulting equations are

A)
B)
C)
D)
E)

Question 45

Using the classical Runge-Kutta method of order 4 with a step size of , the solution of at is

A) 0.099588
B) 0.099668
C) 0.099688
D) 0.099768
E) 0.099788

Question 46

The differential equation is Select all that apply.

A) linear
B) separable
C) exact
D) non-linear
E) Bernoulli

Question 47

The differential equation is Select all that apply.

A) linear
B) separable
C) exact
D) non-linear
E) Bernoulli

Question 48

The solution of the system in the previous problem is

A)
B)
C)
D)
E)