\[ a y(x)+y(x) y'(x)+x=0 \] ✓ Mathematica : cpu = 0.13388 (sec), leaf count = 70
\[\text {Solve}\left [\frac {1}{2} \log \left (\frac {a y(x)}{x}+\frac {y(x)^2}{x^2}+1\right )-\frac {a \tan ^{-1}\left (\frac {a+\frac {2 y(x)}{x}}{\sqrt {4-a^2}}\right )}{\sqrt {4-a^2}}=-\log (x)+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.325 (sec), leaf count = 92
\[\left \{y \left (x \right ) = x \RootOf \left (\textit {\_Z}^{2}+\textit {\_Z} a -{\mathrm e}^{\RootOf \left (\left (a^{2} \left (\tanh ^{2}\left (\frac {\sqrt {\left (a -2\right ) \left (a +2\right )}\, \left (2 c_{1}+\textit {\_Z} +2 \ln \left (x \right )\right )}{2 a}\right )\right )-a^{2}-4 \left (\tanh ^{2}\left (\frac {\sqrt {\left (a -2\right ) \left (a +2\right )}\, \left (2 c_{1}+\textit {\_Z} +2 \ln \left (x \right )\right )}{2 a}\right )\right )-4 \,{\mathrm e}^{\textit {\_Z}}+4\right ) x^{2}\right )}+1\right )\right \}\]