ODE
\[ y'(x)=x \left (x^2 y(x)-y(x)^2+2\right ) \] ODE Classification
[_Riccati]
Book solution method
Riccati ODE, Generalized ODE
Mathematica ✓
cpu = 0.0453608 (sec), leaf count = 63
\[\left \{\left \{y(x)\to \frac {2 c_1 x^2+\sqrt {\pi } x^2 \text {erf}\left (\frac {x^2}{2}\right )+2 e^{-\frac {x^4}{4}}}{2 c_1+\sqrt {\pi } \text {erf}\left (\frac {x^2}{2}\right )}\right \}\right \}\]
Maple ✓
cpu = 0.341 (sec), leaf count = 51
\[ \left \{ y \left ( x \right ) ={\frac {1}{\sqrt {\pi }} \left ( {\it Erf} \left ( {\frac {{x}^{2}}{2}} \right ) \sqrt {\pi }{\it \_C1}\,{x}^{2}+{x}^{2}\sqrt {\pi }+2\,{{\rm e}^{-1/4\,{x}^{4}}}{\it \_C1} \right ) \left ( {\it Erf} \left ( {\frac {{x}^{2}}{2}} \right ) {\it \_C1}+1 \right ) ^{-1}} \right \} \] Mathematica raw input
DSolve[y'[x] == x*(2 + x^2*y[x] - y[x]^2),y[x],x]
Mathematica raw output
{{y[x] -> (2/E^(x^4/4) + 2*x^2*C[1] + Sqrt[Pi]*x^2*Erf[x^2/2])/(2*C[1] + Sqrt[Pi]*Erf[x^2/2])}}
Maple raw input
dsolve(diff(y(x),x) = x*(2+x^2*y(x)-y(x)^2), y(x),'implicit')
Maple raw output
y(x) = (erf(1/2*x^2)*Pi^(1/2)*_C1*x^2+x^2*Pi^(1/2)+2*exp(-1/4*x^4)*_C1)/Pi^(1/2)/(erf(1/2*x^2)*_C1+1)