Here is an even simpler example:
LaplaceTransform[Exp[-t] Cos[2 t], t, s]
returns
(1 + s)/(4 + (1 + s)^2)
as expected. However,
InverseLaplaceTransform[(1 + s)/(4 + (1 + s)^2), s, t]
1/2 E^((-1 - 2 I) t) (1 + E^(4 I t))
Dosen't work with :
InverseLaplaceTransform[BesselK[1, s], s, t] // Simplify (* ? *)
but:
LaplaceTransform[(t HeavisideTheta[-1 + t])/Sqrt[-1 + t^2], t, s] (* BesselK[1, s] *)
Hi, If you use Simplify function, you can get original equation
InverseLaplaceTransform[1/(Sqrt[s] +s), s, t] // Simplify
Hi Les?aw
I do not know what to write here, but from my experience it's normal behavior.Once LaplaceTransform it works and once InverseLaplaceTransform it does not work, or vice versa.Depending on the example.
Maybe someone from Wolfram development team answer your question and better explain you.
Try:
InverseLaplaceTransform[1/(Sqrt[s] + s) // Apart, s, t]
Regards Mariusz.
