\[ \left (y'(x)^2+1\right ) (a y(x)+b)-c=0 \] ✓ Mathematica : cpu = 0.34926 (sec), leaf count = 223
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\frac {\frac {c \sqrt {-a c} \sqrt {\frac {\text {$\#$1} a+b}{c}} \sin ^{-1}\left (\frac {a \sqrt {-\text {$\#$1} a-b+c}}{\sqrt {-a} \sqrt {-a c}}\right )}{\sqrt {-a}}-(\text {$\#$1} a+b) \sqrt {-\text {$\#$1} a-b+c}}{a \sqrt {\text {$\#$1} a+b}}\& \right ][-x+c_1]\right \},\left \{y(x)\to \text {InverseFunction}\left [\frac {\frac {c \sqrt {-a c} \sqrt {\frac {\text {$\#$1} a+b}{c}} \sin ^{-1}\left (\frac {a \sqrt {-\text {$\#$1} a-b+c}}{\sqrt {-a} \sqrt {-a c}}\right )}{\sqrt {-a}}-(\text {$\#$1} a+b) \sqrt {-\text {$\#$1} a-b+c}}{a \sqrt {\text {$\#$1} a+b}}\& \right ][x+c_1]\right \}\right \}\] ✓ Maple : cpu = 0.118 (sec), leaf count = 88
\[\left \{-c_{1}+x -\left (\int _{}^{y \left (x \right )}\frac {\textit {\_a} a +b}{\sqrt {-\left (\textit {\_a} a +b \right ) \left (\textit {\_a} a +b -c \right )}}d \textit {\_a} \right ) = 0, -c_{1}+x -\left (\int _{}^{y \left (x \right )}-\frac {\textit {\_a} a +b}{\sqrt {-\left (\textit {\_a} a +b \right ) \left (\textit {\_a} a +b -c \right )}}d \textit {\_a} \right ) = 0, y \left (x \right ) = \frac {-b +c}{a}\right \}\]