MHB What Is the Guessed Form Using the Method of Undetermined Coefficients?

[Dustinsfl]

$$
A\exp\left(\frac{-t}{2}\right)\sin x\cosh \left(\frac{\sqrt{5}}{2}t\right) + B\exp\left(\frac{-t}{2}\right)\sin x\sinh \left(\frac{\sqrt{5}}{2}t\right)
$$

What would be the guessed form using the method of undetermined coefficients?

Also, if I had
$$
\exp\left(\frac{-t}{2}\right)\sum\left[\sin nx\left(C_n\cos\left(\frac{\sqrt{4n^2-9}}{2}t\right)+D_n\sin\left(\frac{\sqrt{4n^2-9}}{2}t\right)\right)\right],
$$
what would be the guessed form as well?

 

[Sudharaka]

$$
A\exp\left(\frac{-t}{2}\right)\sin x\cosh \left(\frac{\sqrt{5}}{2}t\right) + B\exp\left(\frac{-t}{2}\right)\sin x\sinh \left(\frac{\sqrt{5}}{2}t\right)
$$

What would be the guessed form using the method of undetermined coefficients?

Also, if I had
$$
\exp\left(\frac{-t}{2}\right)\sum\left[\sin nx\left(C_n\cos\left(\frac{\sqrt{4n^2-9}}{2}t\right)+D_n\sin\left(\frac{\sqrt{4n^2-9}}{2}t\right)\right)\right],
$$
what would be the guessed form as well?

Hi dwsmith, :)

I don't understand your question. Are you talking about the method of undetermined coefficients? If so, what is the differential equation?

Kind Regards,
Sudharaka.

 

[MarkFL]

I think what has been provided is the "right-hand side" of the differential equation, and the OP is wanting to know what form the particular solution will take.