Find a general sol'n for the following ODE:

So I use the auxiliary eq:

m^2 - 6m + 9 = 0

m = 3.

So, the homogeneous sol'n, y_c, is:

How'd I complete it?

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- Dec 9th 2007, 10:31 PM #1

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- Dec 10th 2007, 01:41 AM #2

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Good job so far.

What needs to be done next is find the parts of the solution that are linearly independent to . This is done by substituting y= . This will net you both the 2nd part of the homogeneous solution and the particular solution.

y =

y' =

y'' =

So our equation becomes:

=

=

notice that the u term has cancelled out. This will always happen when we make this substitution. In this case the u' term has also been cancelled but this was just lucky.

u'' =

u' = dt

= (I have integrated by parts)

u =

=

The reason for reusing will soon be apparent

u =

y =

=

=