\[ \boxed { \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+ay \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -bx-c=0} \]
Mathematica: cpu = 1.795728 (sec), leaf count = 142 \[ \text {Solve}\left [\left \{x=c_1 e^{b \left (\frac {\log (\text {K$\$$1206119})}{b}-\frac {\log \left (b-a \text {K$\$$1206119}^2\right )}{2 b}\right )}+e^{b \left (\frac {\log (\text {K$\$$1206119})}{b}-\frac {\log \left (b-a \text {K$\$$1206119}^2\right )}{2 b}\right )} \left (\frac {\tan ^{-1}\left (\frac {\sqrt {a} \text {K$\$$1206119}}{\sqrt {b-a \text {K$\$$1206119}^2}}\right )}{\sqrt {a}}-\frac {c \sqrt {b-a \text {K$\$$1206119}^2}}{b \text {K$\$$1206119}}\right ),y(x)=\frac {b x}{a \text {K$\$$1206119}}+\frac {c-\text {K$\$$1206119}^2}{a \text {K$\$$1206119}}\right \},\{y(x),\text {K$\$$1206119}\}\right ] \]
Maple: cpu = 0.655 (sec), leaf count = 416 \[ \left \{ y \left ( x \right ) =2\,{\frac {b{{\rm e}^{{\it RootOf} \left ( \sqrt {a}{\it \_C1}\,b{{\rm e}^{2\,{\it \_Z}}}-a{{\rm e}^{2\,{ \it \_Z}}}bx+\sqrt {a}{\it \_C1}\,{b}^{2}-{{\rm e}^{2\,{\it \_Z}}}{ \it \_Z}\,b-a{{\rm e}^{2\,{\it \_Z}}}c+a{b}^{2}x-{\it \_Z}\,{b}^{2}+ab c \right ) }}x}{ \left ( {{\rm e}^{2\,{\it RootOf} \left ( \sqrt {a}{\it \_C1}\,b{{\rm e}^{2\,{\it \_Z}}}-a{{\rm e}^{2\,{\it \_Z}}}bx+\sqrt {a} {\it \_C1}\,{b}^{2}-{{\rm e}^{2\,{\it \_Z}}}{\it \_Z}\,b-a{{\rm e}^{2 \,{\it \_Z}}}c+a{b}^{2}x-{\it \_Z}\,{b}^{2}+abc \right ) }}+b \right ) \sqrt {a}}}+2\,{\frac {{{\rm e}^{{\it RootOf} \left ( \sqrt {a}{\it \_C1}\,b{{\rm e}^{2\,{\it \_Z}}}-a{{\rm e}^{2\,{\it \_Z}}}bx+\sqrt {a} {\it \_C1}\,{b}^{2}-{{\rm e}^{2\,{\it \_Z}}}{\it \_Z}\,b-a{{\rm e}^{2 \,{\it \_Z}}}c+a{b}^{2}x-{\it \_Z}\,{b}^{2}+abc \right ) }}}{ \left ( { {\rm e}^{2\,{\it RootOf} \left ( \sqrt {a}{\it \_C1}\,b{{\rm e}^{2\,{ \it \_Z}}}-a{{\rm e}^{2\,{\it \_Z}}}bx+\sqrt {a}{\it \_C1}\,{b}^{2}-{ {\rm e}^{2\,{\it \_Z}}}{\it \_Z}\,b-a{{\rm e}^{2\,{\it \_Z}}}c+a{b}^{2 }x-{\it \_Z}\,{b}^{2}+abc \right ) }}+b \right ) \sqrt {a}} \left ( -1/4 \,{\frac { \left ( {{\rm e}^{2\,{\it RootOf} \left ( \sqrt {a}{\it \_C1} \,b{{\rm e}^{2\,{\it \_Z}}}-a{{\rm e}^{2\,{\it \_Z}}}bx+\sqrt {a}{\it \_C1}\,{b}^{2}-{{\rm e}^{2\,{\it \_Z}}}{\it \_Z}\,b-a{{\rm e}^{2\,{ \it \_Z}}}c+a{b}^{2}x-{\it \_Z}\,{b}^{2}+abc \right ) }}+b \right ) ^{2} {{\rm e}^{-2\,{\it RootOf} \left ( \sqrt {a}{\it \_C1}\,b{{\rm e}^{2\,{ \it \_Z}}}-a{{\rm e}^{2\,{\it \_Z}}}bx+\sqrt {a}{\it \_C1}\,{b}^{2}-{ {\rm e}^{2\,{\it \_Z}}}{\it \_Z}\,b-a{{\rm e}^{2\,{\it \_Z}}}c+a{b}^{2 }x-{\it \_Z}\,{b}^{2}+abc \right ) }}}{a}}+c \right ) } \right \} \]