\[ a y(x) (y(x)-x)+y'(x)-1=0 \] ✓ Mathematica : cpu = 0.0452419 (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 = 0.186 (sec), leaf count = 71
\[ \left \{ y \left ( x \right ) ={1 \left ( \sqrt {\pi }{\it Erf} \left ( {\frac {\sqrt {2}x}{2}\sqrt {a}} \right ) \sqrt {2}ax+2\,{a}^{3/2}{\it \_C1}\,x+2\,\sqrt {a}{{\rm e}^{-1/2\,a{x}^{2}}} \right ) \left ( \sqrt {\pi }{\it Erf} \left ( {\frac {\sqrt {2}x}{2}\sqrt {a}} \right ) \sqrt {2}a+2\,{a}^{3/2}{\it \_C1} \right ) ^{-1}} \right \} \]