\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =-x/2+1+ \left ( y \left ( x \right ) \right ) ^{2}+1/2\,{x}^{2}y \left ( x \right ) +axy \left ( x \right ) +1/16\,{x}^{4}+1/4\,a{x}^{3}+1/4\,{a}^{2}{x}^{2}+ \left ( y \left ( x \right ) \right ) ^{3}+3/4\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}+3/2\,ax \left ( y \left ( x \right ) \right ) ^{2}+3/16\,y \left ( x \right ) {x}^{4}+3/4\,y \left ( x \right ) a{x}^{3}+3/4\,{a}^{2}{x}^{2}y \left ( x \right ) +{\frac {{x}^{6}}{64}}+{\frac {3\,{x}^{5}a}{32}}+3/16\,{a}^{2}{x}^{4}+1/8\,{a}^{3}{x}^{3}=0} \]
Mathematica: cpu = 0.144018 (sec), leaf count = 140 \[ \text {Solve}\left [-\frac {1}{3} (27 a+58)^{2/3} \text {RootSum}\left [\text {$\#$1}^3 (27 a+58)^{2/3}-3\ 2^{2/3} \text {$\#$1}+(27 a+58)^{2/3}\& ,\frac {\log \left (\frac {\sqrt [3]{2} \left (\frac {1}{4} \left (6 a x+3 x^2+4\right )+3 y(x)\right )}{\sqrt [3]{27 a+58}}-\text {$\#$1}\right )}{2^{2/3}-\text {$\#$1}^2 (27 a+58)^{2/3}}\& \right ]=\frac {(27 a+58)^{2/3} x}{9\ 2^{2/3}}+c_1,y(x)\right ] \]
Maple: cpu = 0.062 (sec), leaf count = 41 \[ \left \{ y \left ( x \right ) =-{\frac {{x}^{2}}{4}}-{\frac {ax}{2}}+{ \it RootOf} \left ( -x+2\,\int ^{{\it \_Z}}\! \left ( 2\,{{\it \_a}}^{3} +2\,{{\it \_a}}^{2}+a+2 \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) \right \} \]