Hey would you use the Method of Undetermined Coefficients (Method of Good Guessing) to find a particular sol'n to this DE

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- Mar 22nd 2010, 12:07 PMmmattson07Method of Undet Coefficient on this DE?
Hey would you use the Method of Undetermined Coefficients (Method of Good Guessing) to find a particular sol'n to this DE

- Mar 22nd 2010, 02:19 PMmmattson07
And you would have to split the particular solution up because the non homogeneous part is the sum of two terms?

In other words find Yp for then find Yp for and the two of them together make up the particular solution for the original DE? - Mar 22nd 2010, 03:29 PMProve It
- Mar 22nd 2010, 07:26 PMmmattson07
EDIT: I substituted the appropriate Yp's and I got

2C2(sin(2x))+2C1(cos(2x))-10C2(cos(2x))+10C1(sin(2x))=7e^2x + cos(2x).

I'm still unsure how to determine C1 and C2 from this? - Mar 22nd 2010, 10:10 PMmmattson07
Ok so I set the coefficients equal and found and . I believe I need to find a particular solution for the part in which id guess Yp to be

- Mar 23rd 2010, 12:07 PMANDS!
From the homogenous solution to the differential you find that solutions are:

.

However, when you go to solve for the two particular solutions to the differential, you notice that you already have an exponential to the 2x as a solution of your homogenous. So you need to multiple your original "guess" by , where k is the smallest exponent needed to get a unique guess that is not a solution to our homogenous differential.

Therefore I would solve my particular as:

Now substituting into your original d.e.:

Terms cancel out leaving:

Therefore our particular solution for our exponential is - Mar 23rd 2010, 12:55 PMmmattson07
Thanks. I calculated the full solution to be