The reason Mathematica says it got division by zero, because your initial conditions are not valid. They produce no solution.
The analytical solution to
$$
\left( 1+\sqrt {\pi\,x} \right) y \left( x \right) +x{\frac {\rm d}{
{\rm d}x}}y \left( x \right) -1/6\,{x}^{2}{\frac {{\rm d}^{2}}{{\rm d}
{x}^{2}}}y \left( x \right) =0
$$
Is given by Maple as (DSolve does not seem to be able to solve this, after some time waiting).
$$
y \left( x \right) ={\it \_C1}\,{x}^{7/2+1/2\,\sqrt {73}}
{\mbox{$_0$F$_1$}(\ ;\,1+2\,\sqrt {73};\,24\,\sqrt {\pi}\sqrt {x})}+{
\it \_C2}\,{x}^{7/2-1/2\,\sqrt {73}}
{\mbox{$_0$F$_1$}(\ ;\,1-2\,\sqrt {73};\,24\,\sqrt {\pi}\sqrt {x})}
$$
Where $F_1$ is hypergeom function. Taking derivative of the above gives
$$
{\frac {\rm d}{{\rm d}x}}y \left( x \right) ={\frac {{\it \_C1}\,{x}^{
7/2+1/2\,\sqrt {73}} \left( 7/2+1/2\,\sqrt {73} \right)
{\mbox{$_0$F$_1$}(\ ;\,1+2\,\sqrt {73};\,24\,\sqrt {\pi}\sqrt {x})}}{x
}}+12\,{\frac {{\it \_C1}\,{x}^{7/2+1/2\,\sqrt {73}}
{\mbox{$_0$F$_1$}(\ ;\,2+2\,\sqrt {73};\,24\,\sqrt {\pi}\sqrt {x})}
\sqrt {\pi}}{ \left( 1+2\,\sqrt {73} \right) \sqrt {x}}}+{\frac {{\it
\_C2}\,{x}^{7/2-1/2\,\sqrt {73}} \left( 7/2-1/2\,\sqrt {73} \right)
{\mbox{$_0$F$_1$}(\ ;\,1-2\,\sqrt {73};\,24\,\sqrt {\pi}\sqrt {x})}}{x
}}+12\,{\frac {{\it \_C2}\,{x}^{7/2-1/2\,\sqrt {73}}
{\mbox{$_0$F$_1$}(\ ;\,2-2\,\sqrt {73};\,24\,\sqrt {\pi}\sqrt {x})}
\sqrt {\pi}}{ \left( 1-2\,\sqrt {73} \right) \sqrt {x}}}
$$
You can now see that at $x=0$ there is a division by zero.
So your initial conditions are not valid or something wrong with your equations (may be did not copy it correctly from the book?).
