laplace



Hello Ray,
You are correct, it is the documentation in desolv.usg which needs to be 
corrected.  I copied and
pasted the example.
Regarding the other issue,
The commercial macsyma returns
x = (%k3+5*%k2+6*%k1)*%e^-t/2+(-%k3-4*%k2-3*%k1)*%e^-(2*t)+(%k3+3*%k2
+2*%k1)*%e^-(3*t)/2
for ode('diff(x,t,3)+6*'diff(x,t,2)+11*'diff(x,t,1)+6*x,x,t)
but returns
x = %k1*%e^-t+%k2*%e^-(2*t)
for ode('diff(x,t,2)+3*'diff(x,t,1)+2*x,x,t).
There is no reason to have the first expression involve linear 
combinations of constants, except that
laplace is being used, and these combinations are a result of it.

desolve uses laplace also,  so for this example,
desolve(['diff(F(X),X)=G(X),'diff(G(X),X)=F(X)],[F(X),G(X)]);
gives [f(x) = (g(0)+f(0))*%e^x/2-(g(0)-f(0))*%e^-x/2,g(x) = (g(0)+f(0))*%e
^x/2+(g(0)-f(0))*%e^-x/2].
Now g(0)+f(0) and g(0)-f(0) are artifacts of laplace, and could be 
replaced by K1 and K2,
simplifying the expression.  As expressions get more complicated, 
starting with a simple expression
can be the difference between a useful result or a hopelessly 
complicated one.
When exponentialize is set when ilt is called, the result still involves 
the function values and
derivatives at zero, when in my problem, I am really interested in 
determining the constants at time T.

Raymond Toy wrote:

>>>>>>"Dan" == Donna and Dan Stanger <dan.stanger at ieee.org> writes:
>>>>>>            
>>>>>>
>
>    Dan> First, case changes to maxima have broken laplace, so that
>    Dan> laplace('DIFF(f(x),x),x,s) is not recognized,
>    Dan> but laplace('diff(f(x),x,s) is.
>
>Wasn't that the whole point of making maxima case-sensitive?  DIFF is
>not diff, and diff is maxima's differentiation function.
>
>    Dan> Second, I am using desolve to handle systems of equations.
>    Dan> When it encounters real roots, it returns sinh and cosh
>    Dan> instead of exponentials.  It also works in terms of
>
>Can you use exponentialize on the result?
>
>Ray
>
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