\[ y''(x) (a y(x)+b)+c y'(x)^2=0 \] ✓ Mathematica : cpu = 0.302595 (sec), leaf count = 36
\[\left \{\left \{y(x)\to \frac {-b+(c_1 (-(a+c)) (-x-c_2)){}^{\frac {a}{a+c}}}{a}\right \}\right \}\] ✓ Maple : cpu = 0.437 (sec), leaf count = 42
\[ \left \{ y \left ( x \right ) ={\frac {1}{a} \left ( \left ( {\it \_C1}\,x+{\it \_C2} \right ) \left ( a+c \right ) \left ( {\frac {1}{ \left ( a+c \right ) \left ( {\it \_C1}\,x+{\it \_C2} \right ) }} \right ) ^{{\frac {c}{a+c}}}-b \right ) } \right \} \]