# Different Results under Inverse Laplace Transform

I am getting different results from the following commands:

InverseLaplaceTransform[a/Sqrt[(a*u)+(a*u)^2 ],u,t]

InverseLaplaceTransform[a/Sqrt[(a u)* (1 + a u)], u, t]


In the first one, i have $\frac{1}{a}$ multiplicative factor that doesn't appear on the second one. Any ideas?

• Examine the FullForms of the input expressions and apply FullSimplify on both of them and examine the output – Sektor Apr 6 '16 at 14:56
• Can you show us what the output is? It might vary between versions. – Searke Apr 6 '16 at 15:44
• Using the FullForm and FullSimplify i get same result. – Hugo Andrade Apr 6 '16 at 16:48
• Theoutput are: Exp[-t/2a]BesselI[0,t/2]/a on the first one and Exp[-t/2a]BesselI[0,t/2] on the second one I'm using Mathematica 10.1 Student Edition – Hugo Andrade Apr 6 '16 at 16:51