volunteer with access to mathematica

On 7/6/06, Barton Willis <willisb at unk.edu> wrote:
> I'm seeking a volunteer that has access to a recent version of
> Mathematica as well as a basic ability to use it. Specifically
> I need somebody the check to see if Mathematica can solve these two ODEs:
>
> 'diff(y,x,2)-(3
> *x^6+38*x^4+67*x^2+30)*y/(2*x^10+12*x^8+26*x^6+24*x^4+8*x^2);
Hi Barton,

The first equation is not evaluated by Mathematica 5.2:

DSolve[D[y[x], {x, 2}] - (3*x^6 + 38*x^4 + 67*x^2 + 30)*(y[x]/(2*x^10 +
12*x^8 + 26*x^6 + 24*x^4 + 8*x^2)) == 0, y, x]

returns
                  2       4      6
           (30 + 67 x  + 38 x  + 3 x ) y[x]
DSolve[-(------------------------------------) + y''[x] == 0, y, x]
            2       4       6       8      10
         8 x  + 24 x  + 26 x  + 12 x  + 2 x


>
> 'diff(y,x,2)-(29
>
*x^4-696*x^3+6228*x^2-24624*x+36300)*y/(4*(x-7)^2*(x-6)^2*(x-5)^2*(x^2-12*x+34)^2);

>
DSolve[D[y[x], {x, 2}] -
 ((29*x^4 - 696*x^3 + 6228*x^2 -
 24624*x + 36300)*y[x])/
 (4*(x - 7)^2*(x - 6)^2*
 (x - 5)^2*(x^2 - 12*x + 34)^
 2) == 0, y, x]

returns

{{y -> Function[{x},
 ((1 - 6*Sqrt[2] - Sqrt[-7 + x]*
 Sqrt[-5 + x] + Sqrt[2]*
 x)^(3/(2*Sqrt[2]))*
 (-1 - 6*Sqrt[2] +
 Sqrt[-7 + x]*Sqrt[
 -5 + x] + Sqrt[2]*x)^
 (3/(2*Sqrt[2]))*
 (-34 - (-12 + x)*x)^
 ((1/4)*(2 - 3*Sqrt[2]))*
 Sqrt[-(313 + 9*(-12 + x)*x)^
 2]*C[1])/((-7 + x)^(1/4)*
 Sqrt[-6 + x]*(-5 + x)^(1/4)*
 Sqrt[3*Sqrt[2] -
 6*Sqrt[22] -
 2*Sqrt[-7 + x]*Sqrt[
 -5 + x] + Sqrt[22]*x]*
 Sqrt[-3*Sqrt[2] -
 6*Sqrt[22] +
 2*Sqrt[-7 + x]*Sqrt[
 -5 + x] + Sqrt[22]*
 x]) +
 ((1 - 6*Sqrt[2] -
 Sqrt[-7 + x]*Sqrt[
 -5 + x] + Sqrt[2]*x)^
 (3/(2*Sqrt[2]))*
 (-1 - 6*Sqrt[2] +
 Sqrt[-7 + x]*Sqrt[
 -5 + x] + Sqrt[2]*x)^
 (3/(2*Sqrt[2]))*
 Sqrt[-(313 + 9*(-12 + x)*x)^
 2]*Sqrt[-34 + 12*x -
 x^2]*C[2]*Integrate[
 -((Sqrt[-7 + K$2816]*
 (-6 + K$2816)*
 Sqrt[-5 + K$2816]*
 (-3*Sqrt[2] +
 6*Sqrt[22] +
 2*Sqrt[-7 + K$2816]*
 Sqrt[-5 + K$2816] -
 Sqrt[22]*K$2816)*
 (-3*Sqrt[2] -
 6*Sqrt[22] +
 2*Sqrt[-7 + K$2816]*
 Sqrt[-5 + K$2816] +
 Sqrt[22]*K$2816)*
 (-34 - (-12 + K$2816)*
 K$2816)^(3/Sqrt[2]))/
 (((1 - 6*Sqrt[2] - Sqrt[
 -7 + K$2816]*Sqrt[-5 +
 K$2816] + Sqrt[2]*
 K$2816)^(3/Sqrt[2])*
 (-1 - 6*Sqrt[2] + Sqrt[
 -7 + K$2816]*Sqrt[-5 +
 K$2816] + Sqrt[2]*
 K$2816)^(3/Sqrt[2]))*
 ((34 - 12*K$2816 +
 K$2816^2)*(313 - 108*
 K$2816 + 9*K$2816^2)^
 2))), {K$2816, 1, x}])/
 ((-34 - (-12 + x)*x)^
 (3/(2*Sqrt[2]))*
 ((-7 + x)^(1/4)*
 Sqrt[-6 + x]*(-5 + x)^
 (1/4)*Sqrt[3*Sqrt[2] -
 6*Sqrt[22] -
 2*Sqrt[-7 + x]*
 Sqrt[-5 + x] +
 Sqrt[22]*x]*Sqrt[
 -3*Sqrt[2] - 6*Sqrt[22] +
 2*Sqrt[-7 + x]*
 Sqrt[-5 + x] +
 Sqrt[22]*x]))]}}

$Version
5.2 for Microsoft Windows (June 20, 2005)

>
> I know a general solution--I'm only interested in whether
> Mathematica can do them. If it can, I have some others
> that might be more changeling to solve that I might
> ask you to try.
>
> Thanks,
>
> Barton
>
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