\[ a (y(x)-1) y(x) y''(x)+y'(x)^2 (b y(x)+c)+h(y(x))=0 \] ✓ Mathematica : cpu = 0.996556 (sec), leaf count = 226
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}-\frac {(1-K[2])^{\frac {1}{2} \left (\frac {2 b}{a}+\frac {2 c}{a}\right )} K[2]^{-\frac {c}{a}}}{\sqrt {c_1+2 \int _1^{K[2]}-\frac {\exp \left (-\frac {2 (c \log (K[1])-(b+c) \log (1-K[1]))}{a}\right ) h(K[1])}{a (K[1]-1) K[1]}dK[1]}}dK[2]\& \right ][x+c_2]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {(1-K[3])^{\frac {1}{2} \left (\frac {2 b}{a}+\frac {2 c}{a}\right )} K[3]^{-\frac {c}{a}}}{\sqrt {c_1+2 \int _1^{K[3]}-\frac {\exp \left (-\frac {2 (c \log (K[1])-(b+c) \log (1-K[1]))}{a}\right ) h(K[1])}{a (K[1]-1) K[1]}dK[1]}}dK[3]\& \right ][x+c_2]\right \}\right \}\] ✓ Maple : cpu = 3.834 (sec), leaf count = 194
\[ \left \{ \int ^{y \left ( x \right ) }\!{a{\frac {1}{\sqrt {a \left ( {\it \_C1}\,a-2\,\int \!{\frac {h \left ( {\it \_b} \right ) }{{\it \_b}\, \left ( {\it \_b}-1 \right ) } \left ( \left ( {\it \_b}-1 \right ) ^{{\frac {b}{a}}} \right ) ^{2} \left ( \left ( {\it \_b}-1 \right ) ^{{\frac {c}{a}}} \right ) ^{2} \left ( {{\it \_b}}^{{\frac {c}{a}}} \right ) ^{-2}}\,{\rm d}{\it \_b} \right ) }}} \left ( {{\it \_b}}^{{\frac {c}{a}}} \right ) ^{-1} \left ( \left ( {\it \_b}-1 \right ) ^{{\frac {-c-b}{a}}} \right ) ^{-1}}{d{\it \_b}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!-{a{\frac {1}{\sqrt {a \left ( {\it \_C1}\,a-2\,\int \!{\frac {h \left ( {\it \_b} \right ) }{{\it \_b}\, \left ( {\it \_b}-1 \right ) } \left ( \left ( {\it \_b}-1 \right ) ^{{\frac {b}{a}}} \right ) ^{2} \left ( \left ( {\it \_b}-1 \right ) ^{{\frac {c}{a}}} \right ) ^{2} \left ( {{\it \_b}}^{{\frac {c}{a}}} \right ) ^{-2}}\,{\rm d}{\it \_b} \right ) }}} \left ( {{\it \_b}}^{{\frac {c}{a}}} \right ) ^{-1} \left ( \left ( {\it \_b}-1 \right ) ^{{\frac {-c-b}{a}}} \right ) ^{-1}}{d{\it \_b}}-x-{\it \_C2}=0 \right \} \]