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 = 0.204046 (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 = 0.192 (sec), leaf count = 39
\[\left [y \left (x \right ) = \frac {\textit {\_C1}}{x}+\frac {\textit {\_C2} \left (\sqrt {\pi }\, \sqrt {2}\, \erf \left (\frac {\sqrt {2}\, x}{2}\right )-2 x \,{\mathrm e}^{-\frac {x^{2}}{2}}\right )}{x}\right ]\] 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))
Maple raw output
[y(x) = 1/x*_C1+_C2/x*(Pi^(1/2)*2^(1/2)*erf(1/2*2^(1/2)*x)-2*x*exp(-1/2*x^2))]