\[ a y(x) y'(x)-b x-c+y'(x)^2=0 \] ✓ Mathematica : cpu = 1.87123 (sec), leaf count = 154
\[\text {Solve}\left [\left \{x=\left (\frac {\tan ^{-1}\left (\frac {\sqrt {a} K[1]}{\sqrt {b-a K[1]^2}}\right )}{\sqrt {a}}-\frac {c \sqrt {b-a K[1]^2}}{b K[1]}\right ) \exp \left (b \left (\frac {\log (K[1])}{b}-\frac {\log \left (b-a K[1]^2\right )}{2 b}\right )\right )+c_1 \exp \left (b \left (\frac {\log (K[1])}{b}-\frac {\log \left (b-a K[1]^2\right )}{2 b}\right )\right ),y(x)=\frac {b x}{a K[1]}+\frac {c-K[1]^2}{a K[1]}\right \},\{y(x),K[1]\}\right ]\] ✓ Maple : cpu = 0.418 (sec), leaf count = 281
\[\left \{y \left (x \right ) = \frac {2 \left (\left (b x +c \right ) a -\frac {\left (b +{\mathrm e}^{2 \RootOf \left (a \,b^{2} x -a b x \,{\mathrm e}^{2 \textit {\_Z}}+c_{1} \sqrt {a}\, b^{2}+c_{1} \sqrt {a}\, b \,{\mathrm e}^{2 \textit {\_Z}}-\textit {\_Z} \,b^{2}-\textit {\_Z} b \,{\mathrm e}^{2 \textit {\_Z}}+a b c -a c \,{\mathrm e}^{2 \textit {\_Z}}\right )}\right )^{2} {\mathrm e}^{-2 \RootOf \left (a \,b^{2} x -a b x \,{\mathrm e}^{2 \textit {\_Z}}+c_{1} \sqrt {a}\, b^{2}+c_{1} \sqrt {a}\, b \,{\mathrm e}^{2 \textit {\_Z}}-\textit {\_Z} \,b^{2}-\textit {\_Z} b \,{\mathrm e}^{2 \textit {\_Z}}+a b c -a c \,{\mathrm e}^{2 \textit {\_Z}}\right )}}{4}\right ) {\mathrm e}^{\RootOf \left (a \,b^{2} x -a b x \,{\mathrm e}^{2 \textit {\_Z}}+c_{1} \sqrt {a}\, b^{2}+c_{1} \sqrt {a}\, b \,{\mathrm e}^{2 \textit {\_Z}}-\textit {\_Z} \,b^{2}-\textit {\_Z} b \,{\mathrm e}^{2 \textit {\_Z}}+a b c -a c \,{\mathrm e}^{2 \textit {\_Z}}\right )}}{\left (b +{\mathrm e}^{2 \RootOf \left (a \,b^{2} x -a b x \,{\mathrm e}^{2 \textit {\_Z}}+c_{1} \sqrt {a}\, b^{2}+c_{1} \sqrt {a}\, b \,{\mathrm e}^{2 \textit {\_Z}}-\textit {\_Z} \,b^{2}-\textit {\_Z} b \,{\mathrm e}^{2 \textit {\_Z}}+a b c -a c \,{\mathrm e}^{2 \textit {\_Z}}\right )}\right ) a^{\frac {3}{2}}}\right \}\]