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- #1

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?