ODE
\[ x^3 y'(x)+x^2 y''(x)-\left (2-x^2\right ) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0337592 (sec), leaf count = 49
\[\left \{\left \{y(x)\to \frac {\sqrt {2 \pi } c_2 \text {erf}\left (\frac {x}{\sqrt {2}}\right )-2 c_2 e^{-\frac {x^2}{2}} x+2 c_1}{2 x}\right \}\right \}\]
Maple ✓
cpu = 0.049 (sec), leaf count = 35
\[ \left \{ y \left ( x \right ) ={\frac {1}{x} \left ( \sqrt {\pi }{\it Erf} \left ( {\frac {\sqrt {2}x}{2}} \right ) \sqrt {2}{\it \_C2}-2\,{{\rm e}^{-1/2\,{x}^{2}}}{\it \_C2}\,x+{\it \_C1} \right ) } \right \} \] Mathematica raw input
DSolve[-((2 - x^2)*y[x]) + x^3*y'[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (2*C[1] - (2*x*C[2])/E^(x^2/2) + Sqrt[2*Pi]*C[2]*Erf[x/Sqrt[2]])/(2*x)}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+x^3*diff(y(x),x)-(-x^2+2)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (Pi^(1/2)*erf(1/2*2^(1/2)*x)*2^(1/2)*_C2-2*exp(-1/2*x^2)*_C2*x+_C1)/x