\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +ay \left ( x \right ) \left ( y \left ( x \right ) -x \right ) -1=0} \]
Mathematica: cpu = 0.044006 (sec), leaf count = 120 \[ \left \{\left \{y(x)\to \frac {c_1 \left (\sqrt {\frac {\pi }{2}} \sqrt {a} x e^{\frac {a x^2}{2}} \text {erf}\left (\frac {\sqrt {a} x}{\sqrt {2}}\right )+1\right )+a x e^{\frac {a x^2}{2}}}{a \left (\frac {\sqrt {\frac {\pi }{2}} c_1 e^{\frac {a x^2}{2}} \text {erf}\left (\frac {\sqrt {a} x}{\sqrt {2}}\right )}{\sqrt {a}}+e^{\frac {a x^2}{2}}\right )}\right \}\right \} \]
Maple: cpu = 0.156 (sec), leaf count = 71 \[ \left \{ y \left ( x \right ) ={1 \left ( \sqrt {\pi }{\it Erf} \left ( { \frac {\sqrt {2}x}{2}\sqrt {a}} \right ) \sqrt {2}ax+2\,{a}^{3/2}{\it \_C1}\,x+2\,\sqrt {a}{{\rm e}^{-1/2\,a{x}^{2}}} \right ) \left ( \sqrt {\pi }{\it Erf} \left ( {\frac {\sqrt {2}x}{2}\sqrt {a}} \right ) \sqrt {2}a+2\,{a}^{3/2}{\it \_C1} \right ) ^{-1}} \right \} \]
Sage: cpu = 0.068 (sec), leaf count = 0 \[ \left [\left [y\left (x\right ) = \frac {2 \, \sqrt {\frac {1}{2}} a^{\frac {3}{2}} c x e^{\left (\frac {1}{2} \, a x^{2}\right )} + \sqrt {\pi } a x \text {erf}\left (\sqrt {\frac {1}{2}} \sqrt {a} x\right ) e^{\left (\frac {1}{2} \, a x^{2}\right )} + 2 \, \sqrt {\frac {1}{2}} \sqrt {a}}{2 \, \sqrt {\frac {1}{2}} a^{\frac {3}{2}} c e^{\left (\frac {1}{2} \, a x^{2}\right )} + \sqrt {\pi } a \text {erf}\left (\sqrt {\frac {1}{2}} \sqrt {a} x\right ) e^{\left (\frac {1}{2} \, a x^{2}\right )}}\right ], \text {\texttt {riccati}}\right ] \]