Example 12.13.  Show that  [Graphics:Images/LaplaceDiffIntegrateMod_gr_7.gif].

Explore Solution 12.13.

Enter f[t] and compute  [Graphics:../Images/LaplaceDiffIntegrateMod_gr_18.gif].  

[Graphics:../Images/LaplaceDiffIntegrateMod_gr_19.gif]





[Graphics:../Images/LaplaceDiffIntegrateMod_gr_20.gif]



Use the fact that  [Graphics:../Images/LaplaceDiffIntegrateMod_gr_21.gif]  to help solve for [Graphics:../Images/LaplaceDiffIntegrateMod_gr_22.gif].  

[Graphics:../Images/LaplaceDiffIntegrateMod_gr_23.gif]





[Graphics:../Images/LaplaceDiffIntegrateMod_gr_24.gif]



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

[Graphics:../Images/LaplaceDiffIntegrateMod_gr_25.gif]




[Graphics:../Images/LaplaceDiffIntegrateMod_gr_26.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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