Hello,

trying to fix desolve_laplace as described at
http://groups.google.cz/group/sage-support/browse_thread/thread/b6f6b6f056e80149/e2c0cf18cce9926c

It is continuation of ticket http://trac.sagemath.org/sage_trac/ticket/6479
which has been (hope) solved.

The temporary code is http://user.mendelu.cz/marik/temp/desolvers.py
and it has been tested on equations like equations on the bottom of
this post.

I have still a problem: I do not know how to get sage representation
of 'at(....)

current desolve_laplace produce (via maxima) something like
"x*%e^x*('at('diff('f(x),x,1),x=0))-'f(0)*x*%e^x+'f(0)*%e^x"

If I do
A=maxima("'at('diff('f(x),x,1),x=0)")
A.sage()

I expect the corresponding Sage expression but I get errors.

As a result, the new desolve_laplace cannot be used to solve second
order ODE without initial conditions.

Can you help me to came over this step? Thank you.

Robert Marik.

btw: another improvement od desolve_laplace is, that it removes
initial conditions after solving IVP, in the previous version initial
condition persisted in the maxima session - see the Warming message
after desolve_laplace?


---------------------------------------------------------------
Test equations for new desolve_laplace:

u=function('u',x)
print "*******-----------"
eq = diff(u,x,x)  + u == 0
#A=desolve_laplace(eq,u)
#print A

A=desolve_laplace(eq,u,ics=[0,1,2])
print A


eq = diff(u,x) - exp(-x) - u == 0
A = desolve_laplace(eq,u)
print A
A=desolve_laplace(eq,u,ics=[0,3]).expand()
print A
A=desolve(eq,u,ics=[0,3]).expand()
print A
A=desolve_laplace(eq,u).expand()
print A

print "*******"
eq=  diff(u,x) - exp(-x) - u == 0
A=desolve_laplace(eq,u,ics=[0,3])
print A
eq=  diff(u,x) - exp(-x) - u == 0
A=desolve_laplace(eq,u)
print A
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