# [SOLVED]undetermined coefficients

#### dwsmith

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

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

##### Well-known member
MHB Math Helper
$$A\exp\left(\frac{-t}{2}\right)\sin x\cosh \left(\frac{\sqrt{5}}{2}t\right) + B\exp\left(\frac{-t}{2}\right)\sin x\sinh \left(\frac{\sqrt{5}}{2}t\right)$$

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

##### Administrator
Staff member
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.