\[ a x y'(x)+b y(x)+y(x) y'(x)^2=0 \] ✓ Mathematica : cpu = 0.361771 (sec), leaf count = 157
\[\left \{\text {Solve}\left [\frac {(a+2 b) \log \left (-\sqrt {a^2-\frac {4 b y(x)^2}{x^2}}+a+2 b\right )+a \log \left (\sqrt {a^2-\frac {4 b y(x)^2}{x^2}}+a\right )}{4 (a+b)}=-\frac {\log (x)}{2}+c_1,y(x)\right ],\text {Solve}\left [\frac {a \log \left (a-\sqrt {a^2-\frac {4 b y(x)^2}{x^2}}\right )+(a+2 b) \log \left (\sqrt {a^2-\frac {4 b y(x)^2}{x^2}}+a+2 b\right )}{4 (a+b)}=-\frac {\log (x)}{2}+c_1,y(x)\right ]\right \}\] ✓ Maple : cpu = 0.152 (sec), leaf count = 264
\[\frac {x \left (c_{1} \left (-\frac {a x +\sqrt {a^{2} x^{2}-4 b y \relax (x )^{2}}}{2 y \relax (x )}\right )^{-\frac {a}{a +b}} \left (a x +\sqrt {a^{2} x^{2}-4 b y \relax (x )^{2}}\right ) \left (\frac {a \left (a \,x^{2}+\sqrt {a^{2} x^{2}-4 b y \relax (x )^{2}}\, x +2 y \relax (x )^{2}\right )}{2 y \relax (x )^{2}}\right )^{\frac {-a -2 b}{2 a +2 b}}+y \relax (x )^{2}\right )}{y \relax (x )^{2}} = 0\]