Perhaps it is of interest.
I have further generalized the integration of special functions a bit and
implemented integrals of the type c*z^(v-1)*a^(b*z^r+d). These integrals can be
solved in terms of the Incomplete Gamma function.
Here is an example:
(%i14) integrate(exp(1/x)/x,x);
(%o14) gamma_incomplete(0,-1/x)
Now the solution of the ODE of the posting from below is expressed in terms of
the Incomplete Gamma function:
(%i15) 'diff(y,x)=y*exp(1/x);
(%o15) 'diff(y,x,1) = %e^(1/x)*y
(%i16) ode2(%,y,x);
(%o16) y = %e^-gamma_incomplete(-1,-1/x)*%c
Because we have implemented some transformation rules, Maxima can give this
result in terms of the Exponential Integral Ei:
(%i17) %,gamma_expand:true;
(%o17) y = -%c*%e^(x*%e^(1/x)-expintegral_ei(1/x))
In the first posting we have a term Ei(1,-1/x). I think it should be E(1,-1,x).
This is equivalent to -Ei(1/x).
The question was:
> Will it be possible to get the solution of this ode in terms of exponential
> integrals (during or after the call to ode2)?
The answer is yes, when we implement the suggested extensions of SININT.
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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