\[ a y(x) y'(x)-b x-c+y'(x)^2=0 \] ✓ Mathematica : cpu = 1.76594 (sec), leaf count = 142
\[\text {Solve}\left [\left \{x=c_1 e^{b \left (\frac {\log (\text {K$\$$1181115})}{b}-\frac {\log \left (b-a \text {K$\$$1181115}^2\right )}{2 b}\right )}+e^{b \left (\frac {\log (\text {K$\$$1181115})}{b}-\frac {\log \left (b-a \text {K$\$$1181115}^2\right )}{2 b}\right )} \left (\frac {\tan ^{-1}\left (\frac {\sqrt {a} \text {K$\$$1181115}}{\sqrt {b-a \text {K$\$$1181115}^2}}\right )}{\sqrt {a}}-\frac {c \sqrt {b-a \text {K$\$$1181115}^2}}{b \text {K$\$$1181115}}\right ),y(x)=\frac {b x}{a \text {K$\$$1181115}}+\frac {c-\text {K$\$$1181115}^2}{a \text {K$\$$1181115}}\right \},\{y(x),\text {K$\$$1181115}\}\right ]\]
✓ Maple : cpu = 0.258 (sec), leaf count = 416
\[ \left \{ y \left ( x \right ) =2\,{\frac {b{{\rm e}^{{\it RootOf} \left ( \sqrt {a}{\it \_C1}\,b{{\rm e}^{2\,{\it \_Z}}}-a{{\rm e}^{2\,{\it \_Z}}}bx-{{\rm e}^{2\,{\it \_Z}}}{\it \_Z}\,b-a{{\rm e}^{2\,{\it \_Z}}}c+\sqrt {a}{\it \_C1}\,{b}^{2}+a{b}^{2}x-{\it \_Z}\,{b}^{2}+abc \right ) }}x}{ \left ( {{\rm e}^{2\,{\it RootOf} \left ( \sqrt {a}{\it \_C1}\,b{{\rm e}^{2\,{\it \_Z}}}-a{{\rm e}^{2\,{\it \_Z}}}bx-{{\rm e}^{2\,{\it \_Z}}}{\it \_Z}\,b-a{{\rm e}^{2\,{\it \_Z}}}c+\sqrt {a}{\it \_C1}\,{b}^{2}+a{b}^{2}x-{\it \_Z}\,{b}^{2}+abc \right ) }}+b \right ) \sqrt {a}}}+2\,{\frac {{{\rm e}^{{\it RootOf} \left ( \sqrt {a}{\it \_C1}\,b{{\rm e}^{2\,{\it \_Z}}}-a{{\rm e}^{2\,{\it \_Z}}}bx-{{\rm e}^{2\,{\it \_Z}}}{\it \_Z}\,b-a{{\rm e}^{2\,{\it \_Z}}}c+\sqrt {a}{\it \_C1}\,{b}^{2}+a{b}^{2}x-{\it \_Z}\,{b}^{2}+abc \right ) }}}{ \left ( {{\rm e}^{2\,{\it RootOf} \left ( \sqrt {a}{\it \_C1}\,b{{\rm e}^{2\,{\it \_Z}}}-a{{\rm e}^{2\,{\it \_Z}}}bx-{{\rm e}^{2\,{\it \_Z}}}{\it \_Z}\,b-a{{\rm e}^{2\,{\it \_Z}}}c+\sqrt {a}{\it \_C1}\,{b}^{2}+a{b}^{2}x-{\it \_Z}\,{b}^{2}+abc \right ) }}+b \right ) \sqrt {a}} \left ( -1/4\,{\frac { \left ( {{\rm e}^{2\,{\it RootOf} \left ( \sqrt {a}{\it \_C1}\,b{{\rm e}^{2\,{\it \_Z}}}-a{{\rm e}^{2\,{\it \_Z}}}bx-{{\rm e}^{2\,{\it \_Z}}}{\it \_Z}\,b-a{{\rm e}^{2\,{\it \_Z}}}c+\sqrt {a}{\it \_C1}\,{b}^{2}+a{b}^{2}x-{\it \_Z}\,{b}^{2}+abc \right ) }}+b \right ) ^{2}{{\rm e}^{-2\,{\it RootOf} \left ( \sqrt {a}{\it \_C1}\,b{{\rm e}^{2\,{\it \_Z}}}-a{{\rm e}^{2\,{\it \_Z}}}bx-{{\rm e}^{2\,{\it \_Z}}}{\it \_Z}\,b-a{{\rm e}^{2\,{\it \_Z}}}c+\sqrt {a}{\it \_C1}\,{b}^{2}+a{b}^{2}x-{\it \_Z}\,{b}^{2}+abc \right ) }}}{a}}+c \right ) } \right \} \]