EML 5060 Homework Set 3 Fall 2003

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#

41 5.35 5.34 Linear equations#

41 5.53 5.38 Bernoulli equations#

63 6.33 Radioactive decay*#

64 6.59a Air resistance*#

81 8.28 8.18 Vibrational and growth type¹#

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*

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*#

198 22.22 22.12 Solve as 22.12 (required)²

*: Recommended question. Not required if you know you can do it.

#: Make a graph. For problems with more than one unknown parameter, draw the solutions taking one parameter 1 and the rest 0.

¹: Second double dot should be single dot.

²: Solution appears to be wrong.

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:

Also: Make exam 3 of 1998. Give yourself 50 minutes. Include your solutions with homework set I and grade yourself using the solutions on the web after you get it back.