Question

i have no idea what this means:
\[\mathcal L^{-1} \left \{ \frac{1}{(s^2+a^2)(s^2 + b^2)}\right\}, \quad a^2 \ne b^2; \quad ab \ne 0\]

Answer 1

a and b are just constant

Answer 2

so those are just to say that this is not undefined?

Answer 3

they are saying neither of them are 0

Answer 4

and two are not the equal in value

Answer 5

hmm i'll try doing partial fractions normally..

Answer 6

typing "Apart" is way to do partial fraction in wolf

Answer 7

Yes, with partial fraction, you get
\[
\frac{1}{\left(a^2+s^2\right)
\left(b^2+s^2\right)}=\frac{1}{\left(a^2-b^2\right)
\left(b^2+s^2\right)}+\frac{1}{\left(b^2-a^2\right)
\left(a^2+s^2\right)}
\]

Answer 8

how? :O

Answer 9

http://www.wolframalpha.com/input/?i=Apart%5B1%2F%28%28s%5E2%2Ba%5E2%29%28s%5E2%2Bb%5E2%29%29%5D

Answer 10

well i still need to learn how to get the partial fraction of this manually..

Answer 11

usig gaussian i got

coefficient of s^3
A + C = 0

coeff s^2
B+ D = 0

coeff s
Ab^2 + Ca^2 = 0

constant
Bb^2 + Da^2 = 1

Answer 12

do the usual stuff ...
since the s^2 get's cancelled ... divide the numerator ... to get the previous value.