\[ a x y'(x)+b y(x)+y(x) y'(x)^2=0 \] ✓ Mathematica : cpu = 0.327907 (sec), leaf count = 247
\[\left \{\text {Solve}\left [\frac {2 a \tanh ^{-1}\left (\frac {\sqrt {a^2-\frac {4 b y(x)^2}{x^2}}}{a}\right )-2 (a+2 b) \tanh ^{-1}\left (\frac {\sqrt {a^2-\frac {4 b y(x)^2}{x^2}}}{a+2 b}\right )+a \log \left (a+b+\frac {y(x)^2}{x^2}\right )+2 b \log \left (a+b+\frac {y(x)^2}{x^2}\right )+a \log \left (\frac {y(x)^2}{x^2}\right )}{8 (a+b)}=c_1-\frac {\log (x)}{2},y(x)\right ],\text {Solve}\left [\frac {-2 a \tanh ^{-1}\left (\frac {\sqrt {a^2-\frac {4 b y(x)^2}{x^2}}}{a}\right )+2 (a+2 b) \tanh ^{-1}\left (\frac {\sqrt {a^2-\frac {4 b y(x)^2}{x^2}}}{a+2 b}\right )+a \log \left (a+b+\frac {y(x)^2}{x^2}\right )+2 b \log \left (a+b+\frac {y(x)^2}{x^2}\right )+a \log \left (\frac {y(x)^2}{x^2}\right )}{8 (a+b)}=c_1-\frac {\log (x)}{2},y(x)\right ]\right \}\]
✓ Maple : cpu = 0.099 (sec), leaf count = 242
\[ \left \{ {\frac {{\it \_C1}\,x}{ \left ( y \left ( x \right ) \right ) ^{2}} \left ( {\frac {1}{2\,y \left ( x \right ) } \left ( -ax+\sqrt {{a}^{2}{x}^{2}-4\,b \left ( y \left ( x \right ) \right ) ^{2}} \right ) } \right ) ^{-{\frac {a}{a+b}}} \left ( -ax+\sqrt {{a}^{2}{x}^{2}-4\,b \left ( y \left ( x \right ) \right ) ^{2}} \right ) \left ( -{\frac {a}{2\, \left ( y \left ( x \right ) \right ) ^{2}} \left ( -a{x}^{2}+\sqrt {{a}^{2}{x}^{2}-4\,b \left ( y \left ( x \right ) \right ) ^{2}}x-2\, \left ( y \left ( x \right ) \right ) ^{2} \right ) } \right ) ^{-{\frac {a+2\,b}{2\,a+2\,b}}}}+x=0,{\frac {{\it \_C1}\,x}{ \left ( y \left ( x \right ) \right ) ^{2}} \left ( ax+\sqrt {{a}^{2}{x}^{2}-4\,b \left ( y \left ( x \right ) \right ) ^{2}} \right ) \left ( {\frac {a}{2\, \left ( y \left ( x \right ) \right ) ^{2}} \left ( a{x}^{2}+\sqrt {{a}^{2}{x}^{2}-4\,b \left ( y \left ( x \right ) \right ) ^{2}}x+2\, \left ( y \left ( x \right ) \right ) ^{2} \right ) } \right ) ^{-{\frac {a+2\,b}{2\,a+2\,b}}} \left ( -{\frac {1}{2\,y \left ( x \right ) } \left ( ax+\sqrt {{a}^{2}{x}^{2}-4\,b \left ( y \left ( x \right ) \right ) ^{2}} \right ) } \right ) ^{-{\frac {a}{a+b}}}}+x=0 \right \} \]