\[ -h(y(x))-2 (1-2 y(x)) y'(x)^2+3 (1-y(x)) y(x) y''(x)=0 \] ✓ Mathematica : cpu = 0.585538 (sec), leaf count = 186
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}-\frac {1}{(1-K[2])^{2/3} K[2]^{2/3} \sqrt {c_1+2 \int _1^{K[2]}-\frac {\exp \left (-2 \left (\frac {2}{3} \log (1-K[1])+\frac {2}{3} \log (K[1])\right )\right ) h(K[1])}{3 (K[1]-1) K[1]}dK[1]}}dK[2]\& \right ][x+c_2]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(1-K[3])^{2/3} K[3]^{2/3} \sqrt {c_1+2 \int _1^{K[3]}-\frac {\exp \left (-2 \left (\frac {2}{3} \log (1-K[1])+\frac {2}{3} \log (K[1])\right )\right ) h(K[1])}{3 (K[1]-1) K[1]}dK[1]}}dK[3]\& \right ][x+c_2]\right \}\right \}\] ✓ Maple : cpu = 1.339 (sec), leaf count = 119
\[ \left \{ \int ^{y \left ( x \right ) }\!-{\frac {\sqrt {9}}{3}{\frac {1}{\sqrt {{\it \_b}\, \left ( {\it \_b}-1 \right ) \left ( {\it \_C1}-{\frac {2}{3}\int \!{\frac {h \left ( {\it \_b} \right ) }{{\it \_b}\, \left ( {\it \_b}-1 \right ) } \left ( {{\it \_b}}^{2}-{\it \_b} \right ) ^{-{\frac {4}{3}}}}\,{\rm d}{\it \_b}} \right ) \sqrt [3]{{\it \_b}\, \left ( {\it \_b}-1 \right ) }}}}}{d{\it \_b}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!{\frac {\sqrt {9}}{3}{\frac {1}{\sqrt {{\it \_b}\, \left ( {\it \_b}-1 \right ) \left ( {\it \_C1}-{\frac {2}{3}\int \!{\frac {h \left ( {\it \_b} \right ) }{{\it \_b}\, \left ( {\it \_b}-1 \right ) } \left ( {{\it \_b}}^{2}-{\it \_b} \right ) ^{-{\frac {4}{3}}}}\,{\rm d}{\it \_b}} \right ) \sqrt [3]{{\it \_b}\, \left ( {\it \_b}-1 \right ) }}}}}{d{\it \_b}}-x-{\it \_C2}=0 \right \} \]