\[ a y(x) y'(x)^2+b y(x)+y''(x)=0 \] ✓ Mathematica : cpu = 0.452445 (sec), leaf count = 96
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}-\frac {\sqrt {a}}{\sqrt {e^{2 a c_1-a K[1]^2}-b}}dK[1]\& \right ][x+c_2]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\sqrt {a}}{\sqrt {e^{2 a c_1-a K[2]^2}-b}}dK[2]\& \right ][x+c_2]\right \}\right \}\] ✓ Maple : cpu = 0.987 (sec), leaf count = 70
\[\int _{}^{y \relax (x )}\frac {a}{\sqrt {a \left ({\mathrm e}^{-\textit {\_a}^{2} a} c_{1} a -b \right )}}d \textit {\_a} -x -c_{2} = 0\]