\[ \boxed { \left ( ax+b \right ) ^{2}{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( ax+b \right ) \left ( y \left ( x \right ) \right ) ^{3}+c \left ( y \left ( x \right ) \right ) ^{2}=0} \]
Mathematica: cpu = 2.095766 (sec), leaf count = 149 \[ \text {Solve}\left [-\frac {c}{\sqrt {-a (a x+b)^2}}=\frac {2 \exp \left (\frac {1}{2} \left (-\frac {c}{\sqrt {-a (a x+b)^2}}-\frac {\sqrt {-a (a x+b)^2}}{y(x) (-a x-b)}\right )^2\right )}{\sqrt {2 \pi } \text {erfi}\left (\frac {-\frac {c}{\sqrt {-a (a x+b)^2}}-\frac {\sqrt {-a (a x+b)^2}}{y(x) (-a x-b)}}{\sqrt {2}}\right )+2 c_1},y(x)\right ] \]
Maple: cpu = 0.141 (sec), leaf count = 153 \[ \left \{ {\it \_C1}+ \left ( x+{\frac {b}{a}}+{\frac {c\sqrt {\pi } \sqrt {2}}{2}{\it Erf} \left ( {\frac {\sqrt {2} \left ( {a}^{2}x+ab+cy \left ( x \right ) \right ) }{2\, \left ( ax+b \right ) y \left ( x \right ) }{\frac {1}{\sqrt {a}}}} \right ) {{\rm e}^{{\frac { \left ( {a }^{2}x+ab+cy \left ( x \right ) \right ) ^{2}}{2\, \left ( y \left ( x \right ) \right ) ^{2} \left ( ax+b \right ) ^{2}a}}}}{a}^{-{\frac {3}{2 }}}} \right ) {{\rm e}^{-{\frac { \left ( {a}^{2}x+axy \left ( x \right ) +ab+by \left ( x \right ) +cy \left ( x \right ) \right ) \left ( {a}^{2}x -axy \left ( x \right ) +ab-by \left ( x \right ) +cy \left ( x \right ) \right ) }{2\, \left ( y \left ( x \right ) \right ) ^{2} \left ( ax+b \right ) ^{2}a}}}}=0 \right \} \]