Deck 17: Second-Order Differential Equations

Question 1

Solve the differential equation using the m ethod of undetermined

Answer 1

Question 2

Solve the initial-value problem.

Answer 2

Question 3

Answer 3

Question 4

Solve the differential equation using th e method of variation of parameters.

Question 5

Solve the differential equation.

Question 6

Solve the differential equation.

Question 7

Solve the differential equation using the method of variation of parameters.

Question 8

Solve the differential equation.

Question 9

Solve the initial-value problem.

Question 10

Solve the differential equation using the method of undetermined

Question 11

Solve the differential equation using the method of variation of parameters.

Question 12

Solve the boundary-value problem, if possible.

Question 13

Solve the differential equation.

Question 14

Solve the differential equation using th e method of variation of parameters.

Question 15

Solve the boundary-value problem, if possible.

Question 16

Solve the initial-value problem.

Question 17

Question 18

Solve the initial-value problem ethod of undetermined coefficients.

Question 19

Solve the differential equation.

Question 20

Solve the initial-value problem ethod of undetermined

Question 21

A spring with a mass of 2 kg has damping constant 14, and a force of is required to keep the spring stretched beyond its natural length.The spring is stretched 1m beyond its natural length and then released with zero velocity.Find the position of the mass at any time

Question 22

Solve the initial-value problem.

Question 23

Solve the initial-value problem.

Question 24

Solve the differential equation.

Question 25

Solve the initial-value problem using the method of undetermined coefficients.

Question 26

Solve the differential equation.

Question 27

Solve the differential equation using the method of variation of parameters.

Question 28

Solve the differential equation.

Question 29

Solve the initial-value problem.

Question 30

Use power series to solve the differential equation.

Question 31

A mass has natural length m and is maintained stretched to a length of m by a force of If the spring is compressed to a length of m and then released with zero velocity, find the position of the mass at any time .

Question 32

The solution of the initial-value problem is called a Bessel function of order 0.Solve th e initial - value problem to find a power series expansion for

Question 33

Question 34

A spring with a ma is required to keep the spring stretched beyond its natural length.Find the mass that would produce critical damping.

Question 35

Solve the differential equation using the method of variation of parameters.

Question 36

Use power series to solve the differential equation..

Question 37

Solve the differential equation using the method of undeterm

Question 38

Solve the differential equation using the method of variation of parameters.

Question 39

Solve the differential equation using the method of undeterm

Question 40

Suppose a spring has mass M and spring constant and let Suppose that the damping constant is so small that the damping If an external force is applied (the applied frequency equals the natural frequency), use the method of undetermined to find the equation that describes the motion of the mass.

Question 41

Solve the differential equation.

A)
B)
C)
D)
E)None of these

Question 42

Solve the differential equation using the method of variation of parameters.

A)
B)
C)
D)
E)

Question 43

Solve the differential equation using the method of variation of parameters.

A)
B)
C)
D)
E)

Question 44

Solve the differential equation.

A)
B)
C)
D)
E)

Question 45

Suppose a spring has mass M and spring constant k and let Suppose that the damping constant is so small that the damping force is negligible.If an external force is applied (the applied frequency equals the natural frequency), use the method of undetermined coefficients to find the equation that describes the motion of the mass.

A)
B)
C)
D)
E)

Question 46

Use power series to solve the differential equation.

A)
B)
C)
D)
E)

Question 47

The solution of the initial-value problem is called a Bessel function of order 0.Solve the initial - value problem to find a power series expansion for the Bessel function.

A)
B)
C)
D)
E)

Question 48

A spring with a mass of kg has damping constant 28 and spring constant Find the damping constant that would produce critical damping.

A)
B)
C)
D)
E)

Question 49

Find a trial solution for the method of undetermined coefficients.Do not determine the coefficients.

A)
B)
C)
D)
E)

Question 50

A spring with a 3-kg mass is held stretched 0.9 m beyond its natural length by a force of 30 N.If the spring begins at its equilibrium position but a push gives it an initial velocity of m/s, find the position x(t) of the mass after t seconds.

A)
B)
C)
D)
E)

Question 51

Solve the differential equation using the method of undetermined coefficients.

A)
B)
C)
D)
E)

Question 52

Solve the differential equation using the method of variation of parameters.

A)
B)
C)
D)
E)

Question 53

Solve the initial-value problem.

A)
B)
C)
D)
E)None of these

Question 54

Solve the differential equation.

A)
B)
C)
D)
E)

Question 55

A spring with a mass of 2 kg has damping constant 8 and spring constant 80.Graph the position function of the mass at time t if it starts at the equilibrium position with a velocity of 2 m/s.

A)
B)
C)

Question 56

Graph the particular solution and several other solutions.

A)
B)
C)

Question 57

Solve the boundary-value problem, if possible.

A)
B)
C)
D)
E)No solution

Question 58

Solve the differential equation using the method of undetermined coefficients.

A)
B)
C)
D)
E)

Question 59

A series circuit consists of a resistor an inductor with a capacitor with , and a generator producing a voltage of If the initial charge is and the initial current is 0, find the charge at time t.

A)
B)
C)
D)
E)

Question 60

Solve the initial-value problem.

A)
B)
C)
D)
E)

Question 61

A spring with a mass of kg has damping constant 28 and spring constant Find the damping constant that would produce critical damping.

A)
B)
C) 2304
D)
E)

Question 62

Suppose a spring has mass M and spring constant k and let Suppose that the damping constant is so small that the damping force is negligible.If an external force is applied (the applied frequency equals the natural frequency), use the method of undetermined coefficients to find the equation that describes the motion of the mass.

A)
B)
C)
D)
E)

Question 63

Solve the differential equation using the method of variation of parameters.

A)
B)
C)
D)
E)

Question 64

Graph the particular solution and several other solutions.

A)
B)
C)

Question 65

A spring with a mass has natural length m and is maintained stretched to a length of m by a force of N.If the spring is compressed to a length of m and then released with zero velocity, find the position of the mass at any time

A)
B)
C)
D)
E)

Question 66

A series circuit consists of a resistor , an inductor with capacitor with and a battery.If the initial charge is 0.0008 C and the initial current is 0, find the current I(t) at time t.

A)
B)
C)
D)
E)

Question 67

The solution of the initial-value problem is called a Bessel function of order 0.Solve the initial - value problem to find a power series expansion for the Bessel function.

A)
B)
C)
D)
E)

Question 68

Use power series to solve the differential equation.

A)
B)
C)
D)
E)

Question 69

Solve the initial-value problem. .

A)
B)
C)
D)
E)

Question 70

Solve the boundary-value problem, if possible.

A)
B)
C)
D)
E)No solution

Question 71

Solve the differential equation.

A)
B)
C)
D)
E)

Question 72

Use power series to solve the differential equation.

A)
B)
C)
D)
E)

Question 73

Solve the differential equation using the method of undetermined coefficients.

A)
B)
C)
D)
E)

Question 74

A spring with a mass of 2 kg has damping constant 8 and spring constant 80.Graph the position function of the mass at time t if it starts at the equilibrium position with a velocity of 2 m/s.

A)
B)
C)

Question 75

Solve the differential equation.

A)
B)
C)
D)
E)

Question 76

Solve the boundary-value problem, if possible.

A)
B)
C)
D)
E)No solution

Question 77

A spring with a 3-kg mass is held stretched 0.9 m beyond its natural length by a force of 30 N.If the spring begins at its equilibrium position but a push gives it an initial velocity of m/s, find the position x(t) of the mass after t seconds.

A)
B)
C)
D)
E)

Question 78

Solve the initial-value problem.

A)
B)
C)
D)
E)None of these

Question 79

Solve the initial-value problem.

A)
B)
C)
D)
E)

Question 80

Solve the differential equation using the method of undetermined coefficients.

A)
B)
C)
D)
E)