Stewart – Calculus ET 8e Chapter 17 Form A
1. Solve the initial-value problem.
2. Solve the boundary-value problem, if possible.
3. Solve the differential equation.
4. Solve the initial-value problem.
5. Solve the differential equation.
6. Solve the differential equation.
7. Solve the differential equation.
8. Solve the initial-value problem.
9. Solve the boundary-value problem, if possible.
10. Solve the differential equation using the method of variation of parameters.
Stewart – Calculus ET 8e Chapter 17 Form A
11. Solve the differential equation using the method of undetermined coefficients.
12. Solve the initial-value problem using the method of undetermined coefficients.
13. Solve the differential equation using the method of variation of parameters.
14. Solve the differential equation using the method of undetermined coefficients.
15. Solve the initial-value problem using the method of undetermined coefficients.
16. Solve the differential equation using the method of variation of parameters.
17. Solve the differential equation using the method of variation of parameters.
18. Solve the differential equation.
19. A spring with a mass of 2 kg has damping constant 14, and a force of N is required to keep the
spring stretched m beyond its natural length. Find the mass that would produce critical
damping.
20. A series circuit consists of a resistor an inductor with L = H, a capacitor with
C = F, and a -V battery. If the initial charge and current are both 0, find the charge
Q(t) at time t.
Stewart – Calculus ET 8e Chapter 17 Form A
Answer Key
Stewart – Calculus ET 8e Chapter 17 Form A
Stewart – Calculus ET 8e Chapter 17 Form B
1. Solve the initial-value problem.
2. Solve the initial-value problem.
3. Solve the differential equation using the method of variation of parameters.
4. Solve the differential equation using the method of undetermined coefficients.
5. A spring with a -kg 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 .
6. A spring with a mass of kg has damping constant 28 and spring constant . Find the damping
constant that would produce critical damping.
7. 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.
8. Use power series to solve the differential equation..
9. Use power series to solve the differential equation.
Stewart – Calculus ET 8e Chapter 17 Form B
10. 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.
11. Solve the differential equation.
12. Solve the differential equation.
13. Solve the differential equation.
14. Solve the initial-value problem.
15. Solve the differential equation using the method of variation of parameters.
16. Solve the differential equation using the method of undetermined coefficients.
17. Solve the differential equation using the method of variation of parameters.
18. Solve the initial-value problem using the method of undetermined coefficients.
19. A spring with a mass of 2 kg has damping constant 14, and a force of N is required to keep the
spring stretched m beyond its natural length. Find the mass that would produce critical
damping.
Stewart – Calculus ET 8e Chapter 17 Form B
20. A spring with a mass of 2 kg has damping constant 14, and a force of N is required to keep the
spring stretched m beyond its natural length. The spring is stretched 1m beyond its natural
length and then released with zero velocity. Find the position x(t) of the mass at any time t.
Stewart – Calculus ET 8e Chapter 17 Form B
Answer Key
Stewart – Calculus ET 8e Chapter 17 Form B
Stewart – Calculus ET 8e Chapter 17 Form C
____ 1. Solve the differential equation.
a.
b.
c.
d.
e.
____ 2. Solve the differential equation.
a.
b.
c.
d.
e. None of these
Stewart – Calculus ET 8e Chapter 17 Form C
____ 3. Solve the initial-value problem.
a.
b.
c.
d.
e.
____ 4. Solve the initial-value problem.
a.
b.
c.
d.
e. None of these
Stewart – Calculus ET 8e Chapter 17 Form C
____ 5. Solve the boundary-value problem, if possible.
a.
b.
c.
d.
e. No solution
____ 6. Solve the differential equation.
a.
b.
c.
d.
e.
Stewart – Calculus ET 8e Chapter 17 Form C
____ 7. Graph the particular solution and several other solutions.
a.
c.
b.
Stewart – Calculus ET 8e Chapter 17 Form C
____ 8. Solve the differential equation using the method of undetermined coefficients.
a.
b.
c.
d.
e.
____ 9. Find a trial solution for the method of undetermined coefficients. Do not determine the
coefficients.
a.
b.
c.
d.
e.
Stewart – Calculus ET 8e Chapter 17 Form C
____ 10. Solve the differential equation using the method of undetermined coefficients.
a.
b.
c.
d.
e.
____ 11. Solve the differential equation using the method of variation of parameters.
a.
b.
c.
d.
e.
Stewart – Calculus ET 8e Chapter 17 Form C
____ 12. Solve the differential equation using the method of variation of parameters.
a.
b.
c.
d.
e.
____ 13. Solve the differential equation using the method of variation of parameters.
a.
b.
c.
d.
e.
Stewart – Calculus ET 8e Chapter 17 Form C
____ 14. 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.
____ 15. A spring with a mass of kg has damping constant 28 and spring constant . Find the damping
constant that would produce critical damping.
a. 6
b.
6 130
c.
780 6
d.
24 195
e.
Stewart – Calculus ET 8e Chapter 17 Form C
____ 16. 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.
Stewart – Calculus ET 8e Chapter 17 Form C
____ 17. 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.
c.
b.
Stewart – Calculus ET 8e Chapter 17 Form C
____ 18. 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.
____ 19. Use power series to solve the differential equation.
a.
b.
c.
d.
e.