anonymous
  • anonymous
Can anyone find inverse Laplace of this (s^2-pi^2)/(s^2+pi^2)^2
Differential Equations
schrodinger
  • schrodinger
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anonymous
  • anonymous
\[\frac{(s^{2}-\pi ^{2})}{(s ^{2}+\pi ^{2})^{2}}\]
anonymous
  • anonymous
\[\frac{ (s- \pi) (s+ \pi)}{ (s+ \pi) (s+ \pi) }\] now you can do it ;)
Callisto
  • Callisto
The denominator is not quite right?

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anonymous
  • anonymous
thanks itsmylife
anonymous
  • anonymous
i think its done , you gotta separate terms now thats all ;) your welcome @shafqat_uet
anonymous
  • anonymous
holda thers a mistake
anonymous
  • anonymous
in denomirator you made a mistake
anonymous
  • anonymous
\[\frac{ (s - \pi)(s + \pi) }{ (s^2 + \pi^2)(s^2+ \pi^2) } \] this looks pretty easier but m stuck now :(
Callisto
  • Callisto
\[\frac{(s^{2}-\pi ^{2})}{(s ^{2}+\pi ^{2})^{2}}\]\[=\frac{(s^{2})}{(s ^{2}+\pi ^{2})^{2}} - \frac{\pi^2}{{(s ^{2}+\pi ^{2})^{2}}}\] \[=(\frac{s^2}{(s ^{2}+\pi ^{2})})(\frac{1}{(s ^{2}+\pi ^{2})}) - \frac{\pi^2}{{(s ^{2}+\pi ^{2})}}\times \frac{1}{{(s ^{2}+\pi ^{2})}}\]
anonymous
  • anonymous
@itsmylife good try but I have also tried like this. Is it possible using derivative or integral of the laplace
anonymous
  • anonymous
no i guess wat @Callisto has done is quite easier , you gotta take inverse now
Callisto
  • Callisto
Sorry, last step: \[=(\frac{s}{(s ^{2}+\pi ^{2})})(\frac{s}{(s ^{2}+\pi ^{2})}) - \frac{\pi}{{(s ^{2}+\pi ^{2})}}\times \frac{\pi}{{(s ^{2}+\pi ^{2})}}\]

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