ODE
\[ \left (2-a x^2\right ) y'(x)+x y''(x)=0 \] ODE Classification
[[_2nd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0352141 (sec), leaf count = 55
\[\left \{\left \{y(x)\to \sqrt {\frac {\pi }{2}} \sqrt {a} c_1 \text {erfi}\left (\frac {\sqrt {a} x}{\sqrt {2}}\right )-\frac {c_1 e^{\frac {a x^2}{2}}}{x}+c_2\right \}\right \}\]
Maple ✓
cpu = 0.079 (sec), leaf count = 43
\[ \left \{ y \left ( x \right ) ={\frac {1}{x} \left ( -\sqrt {-2\,a}{{\rm e}^{{\frac {a{x}^{2}}{2}}}}{\it \_C2}+x \left ( a{\it \_C2}\,\sqrt {\pi }{\it Erf} \left ( {\frac {x}{2}\sqrt {-2\,a}} \right ) +{\it \_C1} \right ) \right ) } \right \} \] Mathematica raw input
DSolve[(2 - a*x^2)*y'[x] + x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -((E^((a*x^2)/2)*C[1])/x) + C[2] + Sqrt[a]*Sqrt[Pi/2]*C[1]*Erfi[(Sqrt[a]*x)/Sqrt[2]]}}
Maple raw input
dsolve(x*diff(diff(y(x),x),x)+(-a*x^2+2)*diff(y(x),x) = 0, y(x),'implicit')
Maple raw output
y(x) = (-(-2*a)^(1/2)*exp(1/2*a*x^2)*_C2+x*(a*_C2*Pi^(1/2)*erf(1/2*(-2*a)^(1/2)*x)+_C1))/x