Preliminaries.

Example 1. Use pencil and paper techniques and find the general solution to the D. E.
.

Example 2. Use pencil and paper techniques and find the general solution to the I. V. P.
.

Example 3. Use pencil and paper techniques and find the general solution to the I. V. P.
.

Computer Lab Work.

First load Mathematica's Plot Vector Field subroutine.

Example 4. Use Mathematica to find the general solution to the D. E.
.

Example 5. Use Mathematica to find the general solution to the I. V. P.
.

Example 6. Use Mathematica to find the general solution to the I. V. P.
.

Example 7. Use Mathematica's general solution and substitute values C = 0, 1, 2.
Plot the solutions over the interval .

Example 8. Use Mathematica's general solution and make a table of functions
for the values C = -10, -9, ... , -2, -1, 0, 1, 2, ... ,10.
Plot the solutions over the interval .

Example 9. Use Mathematica's Plot Vector Field subroutine and plot the vector slope field for the D. E.
.

Example 10. Plot the solutions you found in 8 and the vector slope field in 9.

(c) John H. Mathews, 1998