[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?

$$\exp\left(\frac{-t}{2}\right)\sum\left[\sin nx\left(C_n\cos\left(\frac{\sqrt{4n^2-9}}{2}t\right)+D_n\sin\left(\frac{\sqrt{4n^2-9}}{2}t\right)\right)\right],$$
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?

$$\exp\left(\frac{-t}{2}\right)\sum\left[\sin nx\left(C_n\cos\left(\frac{\sqrt{4n^2-9}}{2}t\right)+D_n\sin\left(\frac{\sqrt{4n^2-9}}{2}t\right)\right)\right],$$
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.