*Many thanks to Barton Willis,
In this case determining the constants from the boundary
conditions takes some effort. The way both Maple and
MuPAD (I gather that Mathematica does it in a similar
way) handle my problem seems easier.
It is somewhat surprising that, given the fact that maxima
has been around for so many more years than the other
programs, it does not have a similar feature.
Best regards,
Esben Byskov
*
Esben Byskov, Ph.D., Dr.Techn.
Professor Emeritus of Structural Analysis
Department of Civil Engineering
Aalborg University
Sohngaardsholmsvej 57
DK-9000 Aalborg
Denmark
Phone: +45 3963 7328
e-mail: eb at civil.aau.dk
On 2011-01-07 02:01, Barton Willis wrote:
> Maxima has desolve, but for this equation ilt (inverse Laplace transform) is unable to determine the
> needed transform:
>
> (%i11) 'diff((1-1/2*t)*'diff(y(t),t,2),t,2)=1$
>
> (%i12) desolve('diff((1-1/2*t)*'diff(y(t),t,2),t,2)=1,[y(t)]);
> (%o12) y(t)=ilt(-(g35251^5*('diff(laplace(y(t),t,g35251),g35251,1))+y(0)*(-2*g35251^4-g35251^3)-2*(at('diff(y(t),t,1),t=0))*g35251^3+ (at('diff(y(t),t,2),t=0))*(g35251-2*g35251^2)-2*(at('diff(y(t),t,3),t=0))*g35251-2)/(2*g35251^5+2*g35251^4),g35251,t)
>
> A hand solution is something like:
>
> (%i16) ode2(integrate(integrate('diff((1-1/2*t)*'diff(y,t,2),t,2)=1,t),t),y,t);
> (%o16) y=-(((12*%c7+24*%c6+24)*t-24*%c7-48*%c6-48)*log(t-2)+t^3+(6*%c6+6)*t^2+(-12*%c7-24*%c6-24)*t)/6+%k2*t+%k1
>
> You'll need to impose the boundary conditions.
>
> --Barton
>
> -----maxima-bounces at math.utexas.edu wrote: -----
>
>> I don't have access to Maple anymore, but this did the job:
>> diffeqw:= ({diff((1-alpha*xi)*diff(w(xi),xi$2),xi$2) = 1, \
>>
>> w(0)=0, \
>>
>> D(w)(0)=0, \
>>
>> w(1)=0, \
>>
>> D(D(w))(1)=0}, \
>>
>> w(xi));
>>
>>
>>
>> wsol:=dsolve(diffeqw);
>>
>> wsol:=op(2,wsol);