Hello Nijso,
I have done some work on the exponential integrals.
But little work has been done to learn Maxima more about the analysis which can
be done with the exponential integrals. If I try your example I get:
(%i6) 'diff(y,x)=y*exp(1/x);
(%o6) 'diff(y,x,1) = %e^(1/x)*y
(%i7) ode2(%,y,x);
(%o7) y = %c*%e^('integrate(%e^(1/x)/x,x)+x*%e^(1/x))
Thus Maxima can not integrate %e^(1/x)/x. The solution would be your desired
result in terms of the exponential integral ei.
I am interessed to learn more about the algorithm to integrate functions. So
perhaps I would like to find some extensions to support more symbolically
calculations for the implemented special functions like the exponential
integrals.
A fast implementation I have done today would give the integrals of the special
functions themselves. Here are some examples I have got today with an extension
to the routines of sinint:
(%i14) integrate(expintegral_ei(x),x);
(%o14) x*expintegral_ei(x)-%e^x
(%i15) integrate(expintegral_si(x),x);
(%o15) x*expintegral_si(x)+cos(x)
(%i16) integrate(expintegral_si(a*x+b),x);
(%o16) ((a*x+b)*expintegral_si(a*x+b)+cos(a*x+b))/a
Perhaps such an extension would be a first and interessting step to give more
support to the special functions.
Dieter Kaiser
-----Urspr?ngliche Nachricht-----
Von: maxima-bounces at math.utexas.edu [mailto:maxima-bounces at math.utexas.edu] Im
Auftrag von nijso beishuizen
Gesendet: Mittwoch, 29. Oktober 2008 10:05
An: maxima at math.utexas.edu
Betreff: [Maxima] exponential integral as solution of ode?
Hello,
I saw some posts about the exponential integral being implemented.
I am working on a problem now where the exponential integral is the
solution of an ode.
A simple ode that gives Ei as a solution is
de : diff(y(x),x) = y(x)*exp(1/x);
Maple solution:
y(x) = _C1 exp( x exp(1/x) + Ei(1, - 1/x) )
Will it be possible to get the solution of this ode in terms of exponential
integrals (during or after the call to ode2)?
Regards,
Nijso
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