\[ a x y'(x)+b y(x)+y(x) y'(x)^2=0 \] ✓ Mathematica : cpu = 0.632101 (sec), leaf count = 245
\[\left \{\text {Solve}\left [\frac {1}{8} \left (\frac {2 a \tanh ^{-1}\left (\frac {\sqrt {a^2-\frac {4 b y(x)^2}{x^2}}}{a}\right )-2 (a+2 b) \tanh ^{-1}\left (\frac {\sqrt {a^2-\frac {4 b y(x)^2}{x^2}}}{a+2 b}\right )+a \log \left (a+b+\frac {y(x)^2}{x^2}\right )+2 b \log \left (a+b+\frac {y(x)^2}{x^2}\right )+a \log \left (\frac {y(x)^2}{x^2}\right )}{a+b}+4 \log (x)\right )=c_1,y(x)\right ],\text {Solve}\left [\frac {1}{8} \left (\frac {-2 a \tanh ^{-1}\left (\frac {\sqrt {a^2-\frac {4 b y(x)^2}{x^2}}}{a}\right )+2 (a+2 b) \tanh ^{-1}\left (\frac {\sqrt {a^2-\frac {4 b y(x)^2}{x^2}}}{a+2 b}\right )+a \log \left (a+b+\frac {y(x)^2}{x^2}\right )+2 b \log \left (a+b+\frac {y(x)^2}{x^2}\right )+a \log \left (\frac {y(x)^2}{x^2}\right )}{a+b}+4 \log (x)\right )=c_1,y(x)\right ]\right \}\]
✓ Maple : cpu = 0.092 (sec), leaf count = 264
\[ \left \{ {\frac {x}{ \left ( y \left ( x \right ) \right ) ^{2}} \left ( {\it \_C1}\, \left ( -{\frac {1}{2\,y \left ( x \right ) } \left ( ax+\sqrt {{a}^{2}{x}^{2}-4\,b \left ( y \left ( x \right ) \right ) ^{2}} \right ) } \right ) ^{-{\frac {a}{a+b}}} \left ( ax+\sqrt {{a}^{2}{x}^{2}-4\,b \left ( y \left ( x \right ) \right ) ^{2}} \right ) \left ( {\frac {a}{2\, \left ( y \left ( x \right ) \right ) ^{2}} \left ( a{x}^{2}+\sqrt {{a}^{2}{x}^{2}-4\,b \left ( y \left ( x \right ) \right ) ^{2}}x+2\, \left ( y \left ( x \right ) \right ) ^{2} \right ) } \right ) ^{{\frac {-a-2\,b}{2\,a+2\,b}}}+ \left ( y \left ( x \right ) \right ) ^{2} \right ) }=0,-{\frac {x}{ \left ( y \left ( x \right ) \right ) ^{2}} \left ( {\it \_C1}\, \left ( {\frac {1}{2\,y \left ( x \right ) } \left ( -ax+\sqrt {{a}^{2}{x}^{2}-4\,b \left ( y \left ( x \right ) \right ) ^{2}} \right ) } \right ) ^{-{\frac {a}{a+b}}} \left ( ax-\sqrt {{a}^{2}{x}^{2}-4\,b \left ( y \left ( x \right ) \right ) ^{2}} \right ) \left ( -{\frac {a}{2\, \left ( y \left ( x \right ) \right ) ^{2}} \left ( -a{x}^{2}+\sqrt {{a}^{2}{x}^{2}-4\,b \left ( y \left ( x \right ) \right ) ^{2}}x-2\, \left ( y \left ( x \right ) \right ) ^{2} \right ) } \right ) ^{{\frac {-a-2\,b}{2\,a+2\,b}}}- \left ( y \left ( x \right ) \right ) ^{2} \right ) }=0 \right \} \]