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);