\[ \boxed { \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+ \left ( ax+b \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -ay \left ( x \right ) +c=0} \]
Mathematica: cpu = 2.056261 (sec), leaf count = 183 \[ \left \{\left \{y(x)\to \frac {-2 \sqrt {-a^4 e^{2 c_1} x^2-2 a^4 e^{2 c_1} x+a^4 \left (-e^{2 c_1}\right )}+2 a^3 x+a^3-2 a^2 b x-a b^2-a e^{2 c_1}+4 a c}{4 a^2}\right \},\left \{y(x)\to \frac {2 \sqrt {-a^4 e^{2 c_1} x^2-2 a^4 e^{2 c_1} x+a^4 \left (-e^{2 c_1}\right )}+2 a^3 x+a^3-2 a^2 b x-a b^2-a e^{2 c_1}+4 a c}{4 a^2}\right \}\right \} \]
Maple: cpu = 0.468 (sec), leaf count = 50 \[ \left \{ y \left ( x \right ) ={\frac {-{a}^{2}{x}^{2}-2\,abx-{b}^{2}+4 \,c}{4\,a}},y \left ( x \right ) ={\it \_C1}\,x+{\frac {{{\it \_C1}}^{2} +{\it \_C1}\,b+c}{a}} \right \} \]