EML 5060 Homework Set 3 Fall 2000

Page HW Class Topic

6 1.15 1.14 Notations

6 1.17 Notations

6 1.18 Notations

6 1.22 1.21 Notations

6 1.26 Solution by inspection

23 3.40 3.39 Separation of variables

23 3.44 3.42 Separation of variables

23 3.49 3.50 Homogeneous equations

23 3.52 Homogeneous equations

33 4.30 4.32 Exact equations

33 4.34 Exact equations

33 4.39 Exact equations

41 5.35 5.34 Linear equations

41 5.53 5.38 Bernoulli equations

63 6.33 Radioactive decay

64 6.59 Air resistance

66 6.75 RC circuit

81 8.28 8.18 Vibrational and growth type

81 8.23 8.19 Vibrational and growth type

81 8.24 8.21 Vibrational and growth type

86 9.23 Vibrational and growth type

86 9.24 Vibrational and growth type

96 10.44 10.45 Vibrational and growth, forced

96 10.46 Vibrational and growth, forced

96 10.52 10.47 Vibrational and growth, forced

103 11.9 11.10 Vibrational and growth, forced

103 11.14 Vibrational and growth, forced

103 11.26 11.25 Vibrational and growth, forced

107 12.10 12.11 Vibrational and growth, forced

122 13.40 Spring mass system

123 13.53 RCL circuit

124 13.72 Unsteady buoyancy

198 22.22 22.12 Solve as 22.12 (required)

Note: make a graph of the solution for each solved problem.

Also solve the 4 questions below:

1.

Solve the Cauchy equation

by taking as the new independent variable. To eliminate x, use the chain rule of differentiation as in

and once more to find y'' in terms of dy/du and d²y/du². Please do not indicate dy/du also by y'! Solution:

2.

Solve the aerodynamically damped spring-mass system

by taking y as the independent variable and as the dependent variable. To eliminate the remaining dt, (in ), use the chain rule of differentiation. Solution:

3.

Solve the motion of a falling body with aerodynamic drag:

Solution:

4.

Solve the equation for the streamfunction in a Stokes boundary layer:

y'' + 2xy' - 2y = 0.

Note that y=x is one solution. Solution: