7.96 bug in Laplace, Maple V.5 (18.2.00)

7.96.1 Ray Vickson

The following behavior is almost unbelievable:

> restart: 
> with(inttrans): 
> f1:=(s+1)/(s*(s^2+6*s+9)); 
 
                                   s + 1 
                        f1 := ---------------- 
                                  2 
                              s (s  + 6 s + 9) 
 
> f2:=1/(s*(s^2+6*s+9)); 
 
                                     1 
                        f2 := ---------------- 
                                  2 
                              s (s  + 6 s + 9) 
 
> invlaplace(f1,s,t); 
 
                1/9 + 2/3 t exp(-3 t) - 1/9 exp(-3 t) 
 
> invlaplace(f2,s,t); 
Error, (in tablelook) division by zero
 

Try as I might, I cannot trace the source of the problem. How can something so simple fail so badly?

It is corrected with Maple 6. (U. Klein)

7.96.2 SCHADE, GEORGE (21.2.00)

I tried this on windows 95, release 4, and it worked fine.

7.96.3 Harald Pleym (21.2.00)

I don’t know why, but I know that Maple6 (version 16401) produce the same unbelievable error.

A work around is

> invlaplace(convert(f2,parfrac,s),s,t); 
 
                                   1/9-1/3*t*exp(-3*t)-1/9*exp(-3*t)
 

7.96.4 jmw (21.2.00)

Yet when f2 is expressed differently, things seem to work:

with(inttrans): 
 
f2:=1/(s*(s+3)^2); 
                                      1 
                            f2 := ---------- 
                                           2 
                                  s (s + 3) 
 > invlaplace(f2,s,t); 
 
                     1/9 - 1/9 (1 + 3 t) exp(-3 t)
 

7.96.5 Willard, Daniel Dr (21.2.00)

Just for kicks, I tried f3:=1/((s+a)*(s^2+6*s+9)) and took (limit(invlaplace(f3,s,t),a=0)). That works.

7.96.6 Wilhelm Werner (24.2.00)

Maybe the following gives a hint to what is happening:

>with(inttrans): f2:=1/(s*(s^2+a*s+b));invlaplace(f2,s,t); 
 
                    exp((- 1/2 a + 1/2 %1) t)   exp((- 1/2 a - 1/2 %1) t) 
                    ------------------------- - ------------------------- 
                        - 1/2 a + 1/2 %1            - 1/2 a - 1/2 %1 
              1/b + ----------------------------------------------------- 
                                             2 
                                       sqrt(a  - 4 b) 
 
                                               2 
                                   %1 := sqrt(a  - 4 b)
 

It seems to me that Maple looks into a table containing the above formula and then substitutes a=6 and b=9 (instead of using something like l'Hospitals rule in this case).