\[ a y(x) y'(x)-b x-c+y'(x)^2=0 \] ✓ Mathematica : cpu = 1.53879 (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 = 0.592 (sec), leaf count = 281
\[y \relax (x ) = \frac {2 \,{\mathrm e}^{\RootOf \left (\sqrt {a}\, c_{1} b \,{\mathrm e}^{2 \textit {\_Z}}-{\mathrm e}^{2 \textit {\_Z}} a b x +\sqrt {a}\, c_{1} b^{2}-{\mathrm e}^{2 \textit {\_Z}} \textit {\_Z} b -{\mathrm e}^{2 \textit {\_Z}} a c +a \,b^{2} x -\textit {\_Z} \,b^{2}+a b c \right )} \left (-\frac {\left ({\mathrm e}^{2 \RootOf \left (\sqrt {a}\, c_{1} b \,{\mathrm e}^{2 \textit {\_Z}}-{\mathrm e}^{2 \textit {\_Z}} a b x +\sqrt {a}\, c_{1} b^{2}-{\mathrm e}^{2 \textit {\_Z}} \textit {\_Z} b -{\mathrm e}^{2 \textit {\_Z}} a c +a \,b^{2} x -\textit {\_Z} \,b^{2}+a b c \right )}+b \right )^{2} {\mathrm e}^{-2 \RootOf \left (\sqrt {a}\, c_{1} b \,{\mathrm e}^{2 \textit {\_Z}}-{\mathrm e}^{2 \textit {\_Z}} a b x +\sqrt {a}\, c_{1} b^{2}-{\mathrm e}^{2 \textit {\_Z}} \textit {\_Z} b -{\mathrm e}^{2 \textit {\_Z}} a c +a \,b^{2} x -\textit {\_Z} \,b^{2}+a b c \right )}}{4}+a \left (b x +c \right )\right )}{a^{\frac {3}{2}} \left ({\mathrm e}^{2 \RootOf \left (\sqrt {a}\, c_{1} b \,{\mathrm e}^{2 \textit {\_Z}}-{\mathrm e}^{2 \textit {\_Z}} a b x +\sqrt {a}\, c_{1} b^{2}-{\mathrm e}^{2 \textit {\_Z}} \textit {\_Z} b -{\mathrm e}^{2 \textit {\_Z}} a c +a \,b^{2} x -\textit {\_Z} \,b^{2}+a b c \right )}+b \right )}\]