HomogeneousMod2003.nb

Module for Second Order Homogeneous Linear Differential Equations

Numerical Methods for O. D. E. using Mathematica. (c) John H. Mathews, 2003

Preliminaries.

Use Mathematica to find the general solution to the following differential equations, and the specified family of solutions. Then plot simultaneously this family of solutions.

Example 1.  Find the solutions to the D. E.



with the initial conditions  ,  and    for  m = -10, -8, -6, ... , 6, 8, 10.

Solution 1.

Example 2.  Find the solutions to the D. E.



with the initial conditions  ,  for  c = 0, 1, ... , 8, 9, 10  and   .

Solution 2.

Example 3.  Find the solutions to the D. E.



with the initial conditions    and    for  m = -5, -4, -3, ... , 3, 4, 5.

Solution 3.

Example 4.  Find the solutions to the D. E.



with the initial conditions    for  c = 0, 1, ... , 8, 9, 10  and  .

Solution 4.

Example 5.  Find the solutions to the

    D. E.

with the initial conditions    and    for  m = -5, -4, -3, ... , 3, 4, 5.

Solution 5.

Example 6.  Find the solutions to the D. E.



with the initial conditions    for  c = 0, 1, ... , 8, 9, 10  and  .

Solution 6.

Example 7. Find the general solution to the D. E.

.

Solution 7.

Example 8. Find the general solution to the D. E.

.

Solution 8.

Example 9. Find the general solution to the differential equation

.

Solution 9.

Example 10. Find the general solution to the differential equation

.

Solution 10.

Example 11. Find the general solution to the differential equation

.

Solution 11.

Example 12. Find the general solution to the differential equation

.

Solution 12.

Research Experience for Undergraduates

Converted by Mathematica January 28, 2003