Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Of $\displaystyle \frac{1}{4s^{2}-8s}$

I am approaching the partial fraction $$\displaystyle \frac{1}{4s\left(s-2\right)}=\frac{A}{4s}+\frac{B}{s-2},\text{ where }A=-\frac{1}{2},B=\frac{1}{8}$$

Memorizing the table, I have $$\displaystyle f(t)=-\frac{1}{8}+\frac{1}{8}e^{2t}$$

However, the answer seems to be $$\displaystyle \frac{1}{4}e^{t}\sinh{t}$$

How come?

share|improve this question
3  
The two answers agree: just expand $\text{sinh}t$ –  awllower Mar 19 '13 at 4:21
add comment

1 Answer 1

$$\frac{1}{4}e^{t}\sinh{(t)} = \frac{1}{4}e^{t}\left(\frac{e^t - e^{-t}}{2}\right)= \frac{e^{2t}}{8} -\frac{1}{8} \\$$
So both the book and you are correct.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.