Preliminaries. We wish to solve the first order linear D. E. with a given I. C.
,
the integrating factor is .

Computer Lab Work.

Example 1. Use Mathematica to solve the first order linear D. E. with the given I. C.
with y(0) = 3.
Plot the solution over the interval [0, 3].

First enter the functions p[x] and q[x] and the initial condition.

Construct the integrating factor.

Construct the general solution.

Solve for the constant c.

Form the particular solution from the general solution.

Verify that this is the correct solution to the D. E.

Verify that it has the correct I. V. and plot the solution.

Example 2. Use Mathematica to solve the first order linear D. E. with the given I. C.
with y(0) = 1.
Plot the solution over the interval [0, 3].

First enter the functions p[x] and q[x] and the initial condition.

Construct the integrating factor.

Construct the general solution.

Solve for the constant.

Form the particular solution from the general solution.

Verify that this is the correct solution to the D. E.

Verify that it has the correct I. V. and plot the solution.

(c) John H. Mathews, 1998