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?
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.
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' = dt
= (I have integrated by parts)
The reason for reusing will soon be apparent