Up: Return

Page HW Class

6 1.15 1.14 Notations

6 1.16 Notations

6 1.22 1.21 Notations

6 1.26 Solution by inspection

23 3.35 3.39 Separation of variables

23 3.41 3.42 Separation of variables

23 3.52 3.50 Homogeneous equations

23 3.53 Homogeneous equations

33 4.34 4.32 Exact equations

33 4.39 Exact equations

42 5.56 5.34 Linear equations

42 5.53 5.38 Bernoulli equations

63 6.45 Heat conduction

64 6.62 Air resistance

66 6.88 Product sales

81 8.25 8.18 Constant coefficient equations

81 8.26 8.19 Constant coefficient equations

81 8.34 8.21 Constant coefficient equations

86 9.22 Constant coefficient equations

86 9.23 Constant coefficient equations

96 10.44 10.45 Constant coefficient equations

96 10.52 10.47 Constant coefficient equations

102 11.11 11.10 Constant coefficient equations

102 11.14 Constant coefficient equations

102 11.27 11.25 Constant coefficient equations

107 12.10 12.11 Constant coefficient equations

121 13.33 Spring mass system

122 13.36 Spring mass system

123 13.56 RCL circuit

124 13.70 Unsteady buoyancy

197 22.13 22.12 Solve as a system (required) Solve the 4 questions below

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

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 . 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:

   

   Note that y=x is one solution. Solution:

   

Up: Return