\[ \boxed { \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+a{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +by \left ( x \right ) =0} \]
Mathematica: cpu = 0.313040 (sec), leaf count = 110 \[ \left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {\sqrt {a^2-4 \text {$\#$1} b}+a \log \left (\sqrt {a^2-4 \text {$\#$1} b}-a\right )}{2 b}\& \right ]\left [c_1+\frac {x}{2}\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\frac {\sqrt {a^2-4 \text {$\#$1} b}-a \log \left (\sqrt {a^2-4 \text {$\#$1} b}+a\right )}{2 b}\& \right ]\left [c_1-\frac {x}{2}\right ]\right \}\right \} \]
Maple: cpu = 0.796 (sec), leaf count = 215 \[ \left \{ y \left ( x \right ) =-{\frac {1}{4\,b}{{\rm e}^{-{\frac {1}{2 \,a} \left ( a\ln \left ( -{\frac {1}{4\,b}} \right ) +2\,a{\it lambertW } \left ( 2\,{\frac {{{\rm e}^{-1}}}{a}{{\rm e}^{{\frac {{\it \_C1}\,b }{a}}}}{\frac {1}{\sqrt {-{b}^{-1}}}} \left ( {{\rm e}^{{\frac {bx}{a}} }} \right ) ^{-1}} \right ) -2\,{\it \_C1}\,b+2\,bx+2\,a \right ) }}} \left ( {{\rm e}^{-{\frac {1}{2\,a} \left ( a\ln \left ( -{\frac {1}{4 \,b}} \right ) +2\,a{\it lambertW} \left ( 2\,{\frac {{{\rm e}^{-1}}}{a} {{\rm e}^{{\frac {{\it \_C1}\,b}{a}}}}{\frac {1}{\sqrt {-{b}^{-1}}}} \left ( {{\rm e}^{{\frac {bx}{a}}}} \right ) ^{-1}} \right ) -2\,{\it \_C1}\,b+2\,bx+2\,a \right ) }}}+2\,a \right ) },y \left ( x \right ) =-{ \frac {1}{4\,b}{{\rm e}^{{\it RootOf} \left ( -a\ln \left ( -{\frac { \left ( {{\rm e}^{{\it \_Z}}}+2\,a \right ) ^{2}}{4\,b}} \right ) +2\,{ \it \_C1}\,b-2\,bx+2\,{{\rm e}^{{\it \_Z}}}+2\,a \right ) }} \left ( { {\rm e}^{{\it RootOf} \left ( -a\ln \left ( -{\frac { \left ( {{\rm e}^{ {\it \_Z}}}+2\,a \right ) ^{2}}{4\,b}} \right ) +2\,{\it \_C1}\,b-2\,bx+ 2\,{{\rm e}^{{\it \_Z}}}+2\,a \right ) }}+2\,a \right ) } \right \} \]