Example 12.18.   Show that  [Graphics:Images/LaplaceShiftingMod_gr_46.gif].  

Explore Solution 12.18.

Use Theorem 12.16 and find  [Graphics:../Images/LaplaceShiftingMod_gr_50.gif].  
Enter the function  [Graphics:../Images/LaplaceShiftingMod_gr_51.gif],  and apply Theorem 12.16.

[Graphics:../Images/LaplaceShiftingMod_gr_52.gif]




[Graphics:../Images/LaplaceShiftingMod_gr_53.gif]

 

 

 

 

Aside. We can check this with Mathematica's  result using the LaplaceTransform package.

[Graphics:../Images/LaplaceShiftingMod_gr_54.gif]




[Graphics:../Images/LaplaceShiftingMod_gr_55.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) 2006 John H. Mathews, Russell W. Howell