\[ \left (y'(x)^2+1\right ) (a y(x)+b)-c=0 \] ✓ Mathematica : cpu = 0.975811 (sec), leaf count = 141
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\frac {c \tan ^{-1}\left (\frac {\sqrt {\text {$\#$1} a+b}}{\sqrt {-\text {$\#$1} a-b+c}}\right )-\sqrt {\text {$\#$1} a+b} \sqrt {-\text {$\#$1} a-b+c}}{a}\& \right ]\left [c_1-x\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\frac {c \tan ^{-1}\left (\frac {\sqrt {\text {$\#$1} a+b}}{\sqrt {-\text {$\#$1} a-b+c}}\right )-\sqrt {\text {$\#$1} a+b} \sqrt {-\text {$\#$1} a-b+c}}{a}\& \right ]\left [c_1+x\right ]\right \}\right \}\] ✓ Maple : cpu = 1.636 (sec), leaf count = 88
\[ \left \{ x-\int ^{y \left ( x \right ) }\!{(a{\it \_a}+b){\frac {1}{\sqrt {- \left ( a{\it \_a}+b \right ) \left ( a{\it \_a}+b-c \right ) }}}}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!-{(a{\it \_a}+b){\frac {1}{\sqrt {- \left ( a{\it \_a}+b \right ) \left ( a{\it \_a}+b-c \right ) }}}}{d{\it \_a}}-{\it \_C1}=0,y \left ( x \right ) ={\frac {-b+c}{a}} \right \} \]