\[ \boxed { y \left ( x \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+ax{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +by \left ( x \right ) =0} \]
Mathematica: cpu = 0.945120 (sec), leaf count = 317 \[ \left \{\text {Solve}\left [\frac {\left (\sqrt {a^2-\frac {4 b y(x)^2}{x^2}}-a\right ) \left (\sqrt {a^2-\frac {4 b y(x)^2}{x^2}}+a+2 b\right ) \left (a \log \left (\sqrt {a^2-\frac {4 b y(x)^2}{x^2}}-a\right )+(a+2 b) \log \left (\sqrt {a^2-\frac {4 b y(x)^2}{x^2}}+a+2 b\right )\right )}{8 b (a+b) \left (\sqrt {a^2-\frac {4 b y(x)^2}{x^2}}-a-\frac {2 y(x)^2}{x^2}\right )}=c_1-\frac {\log (x)}{2},y(x)\right ],\text {Solve}\left [\frac {\left (-\sqrt {a^2-\frac {4 b y(x)^2}{x^2}}+a+2 b\right ) \left (\sqrt {a^2-\frac {4 b y(x)^2}{x^2}}+a\right ) \left (a \log \left (\sqrt {a^2-\frac {4 b y(x)^2}{x^2}}+a\right )+(a+2 b) \log \left (\sqrt {a^2-\frac {4 b y(x)^2}{x^2}}-a-2 b\right )\right )}{8 b (a+b) \left (\sqrt {a^2-\frac {4 b y(x)^2}{x^2}}+a+\frac {2 y(x)^2}{x^2}\right )}=c_1-\frac {\log (x)}{2},y(x)\right ]\right \} \]
Maple: cpu = 0.639 (sec), leaf count = 242 \[ \left \{ {\frac {{\it \_C1}\,x}{ \left ( y \left ( x \right ) \right ) ^{ 2}} \left ( -{\frac {1}{2\,y \left ( x \right ) } \left ( ax+\sqrt {{a}^{2 }{x}^{2}-4\,b \left ( y \left ( x \right ) \right ) ^{2}} \right ) } \right ) ^{-{\frac {a}{a+b}}} \left ( ax+\sqrt {{a}^{2}{x}^{2}-4\,b \left ( y \left ( x \right ) \right ) ^{2}} \right ) \left ( {\frac {a}{2 \, \left ( y \left ( x \right ) \right ) ^{2}} \left ( a{x}^{2}+\sqrt {{a} ^{2}{x}^{2}-4\,b \left ( y \left ( x \right ) \right ) ^{2}}x+2\, \left ( y \left ( x \right ) \right ) ^{2} \right ) } \right ) ^{-{\frac {a+2\,b}{ 2\,a+2\,b}}}}+x=0,{\frac {{\it \_C1}\,x}{ \left ( y \left ( x \right ) \right ) ^{2}} \left ( -{\frac {a}{2\, \left ( y \left ( x \right ) \right ) ^{2}} \left ( -a{x}^{2}+\sqrt {{a}^{2}{x}^{2}-4\,b \left ( y \left ( x \right ) \right ) ^{2}}x-2\, \left ( y \left ( x \right ) \right ) ^{2} \right ) } \right ) ^{-{\frac {a+2\,b}{2\,a+2\,b}}} \left ( -ax+\sqrt {{a}^{2}{x}^{2}-4\,b \left ( y \left ( x \right ) \right ) ^{2}} \right ) \left ( {\frac {1}{2\,y \left ( x \right ) } \left ( -ax+\sqrt {{a}^{2}{x}^{2}-4\,b \left ( y \left ( x \right ) \right ) ^{2}} \right ) } \right ) ^{-{\frac {a}{a+b}}}}+x=0 \right \} \]