Background. Use the method of undetermined coefficients.

Computer Lab Work.

Example 1. (a) Use the method of undetermined coefficients to find the general solution to the D. E.

y''''[t] + 2y''[t] + y[t] + 2Sin[t] - 4Cos[t] = 0

1. (b) Find the solution with the I.C.'s

y[0] = 2, y'[0] = -1, y''[0] = 4, y'''[0] = 1,

and plot this solution over the intervals [0, 3], [0, 10] and [0, 30].

First, find the roots of the characteristic equation.

Second, form the the solution to the homogeneous D. E., and check it out.

Third, find the particular solution to the D. E.

Fourth, form the linear system to be solved and solve it.

Fifth, form particular solution, and check it out.

Sixth, form the general solution.

Seventh, form the linear system for the initial conditions and solve it.

Eighth, form the solution, check it out, and plot it.

After you have done all of the above, you are welcome to check your work with Mathematica's built in procedure DSolve.

Example 2. (a) Use the method of undetermined coefficients to find the general solution to the D. E.



2. (b) Find the solution with the I.C.'s

,

and plot this solution over the interval [0, 3].

First, find the roots of the characteristic equation.

Second, form the the solution to the homogeneous D. E., and check it out.

Third, find the particular solution to the D. E.

Fourth, form the linear system to be solved and solve it.

Fifth, form particular solution, and check it out.

Sixth, form the general solution.

Seventh, form the linear system for the initial conditions and solve it.

Eighth, form the solution, check it out, and plot it.

After you have done all of the above, you are welcome to check your work with Mathematica's built in procedure DSolve.

(c) John H. Mathews, 1998