ODE
\[ \left (2-a x^2\right ) y(x)+x y'(x)+x=0 \] ODE Classification
[_linear]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.183791 (sec), leaf count = 70
\[\left \{\left \{y(x)\to \frac {-\frac {\sqrt {2 \pi } e^{\frac {a x^2}{2}} \text {erf}\left (\frac {\sqrt {a} x}{\sqrt {2}}\right )}{a^{3/2}}+2 c_1 e^{\frac {a x^2}{2}}+\frac {2 x}{a}}{2 x^2}\right \}\right \}\]
Maple ✓
cpu = 0.023 (sec), leaf count = 50
\[\left [y \left (x \right ) = \frac {\left (\frac {{\mathrm e}^{-\frac {a \,x^{2}}{2}} x}{a}-\frac {\sqrt {\pi }\, \sqrt {2}\, \erf \left (\frac {\sqrt {2}\, \sqrt {a}\, x}{2}\right )}{2 a^{\frac {3}{2}}}+\textit {\_C1} \right ) {\mathrm e}^{\frac {a \,x^{2}}{2}}}{x^{2}}\right ]\] Mathematica raw input
DSolve[x + (2 - a*x^2)*y[x] + x*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> ((2*x)/a + 2*E^((a*x^2)/2)*C[1] - (E^((a*x^2)/2)*Sqrt[2*Pi]*Erf[(Sqrt[a]*x)/Sqrt[2]])/a^(3/2))/(2*x^2)}}
Maple raw input
dsolve(x*diff(y(x),x)+x+(-a*x^2+2)*y(x) = 0, y(x))
Maple raw output
[y(x) = (exp(-1/2*a*x^2)*x/a-1/2/a^(3/2)*Pi^(1/2)*2^(1/2)*erf(1/2*2^(1/2)*a^(1/2)*x)+_C1)*exp(1/2*a*x^2)/x^2]