University of Florida/Egm4313/s12.team8.dupre/R3.4

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Problem 3.4

Problem Statement[edit]

Use the Basic Rule and the Sum Rule to show that the appropriate particular solution to

(4.1)

is of the form



with n=5, i.e,

.

Solution[edit]

The Basic rule and Sum rule allow us to choose our particular y forms from table 2.1 on page 82 in the Kreyszig Advanced Engineering Mathematics book. These rules state that, using your given , you can find what you should choose to use.

From (4.1), we know that:

(4.2)

Referring to table 2.1, and knowing that the Basic rule tells us that we can match up the form of our to one in the table, and use the accordingly, we find the following two equations:

The for is:

(4.3)

And the for is:

(4.4)

The sum rule tells us that we are able to add these equations, (4.3) and (4.4), to obtain a final solution for . The solution for this is as follows:



Adding similar variables gives us:

(4.5)

Since these k and K values are just constants, we can set:













Our FINAL solution for the of (4.1) is:

(4.6)

And, as was the original problem statement, equation (4.6) is of the form: