\[ -h(y(x))+3 (1-y(x)) y(x) y''(x)-2 (1-2 y(x)) y'(x)^2=0 \] ✓ Mathematica : cpu = 22.76 (sec), leaf count = 182
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}} -\frac {1}{(1-K[2])^{2/3} K[2]^{2/3} \sqrt {2 \int _1^{K[2]} -\frac {h(K[1]) \exp \left (-2 \left (\frac {2}{3} \log (1-K[1])+\frac {2}{3} \log (K[1])\right )\right )}{3 (K[1]-1) K[1]} \, dK[1]+c_1}} \, dK[2]\& \right ]\left [c_2+x\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}} \frac {1}{(1-K[3])^{2/3} K[3]^{2/3} \sqrt {2 \int _1^{K[3]} -\frac {h(K[1]) \exp \left (-2 \left (\frac {2}{3} \log (1-K[1])+\frac {2}{3} \log (K[1])\right )\right )}{3 (K[1]-1) K[1]} \, dK[1]+c_1}} \, dK[3]\& \right ]\left [c_2+x\right ]\right \}\right \}\] ✓ Maple : cpu = 0.329 (sec), leaf count = 119
\[ \left \{ \int ^{y \left ( x \right ) }\!-{\frac {\sqrt {9}}{3}{\frac {1}{\sqrt { \left ( {\it \_b}-1 \right ) \sqrt [3]{{\it \_b}\, \left ( {\it \_b}-1 \right ) }{\it \_b}\, \left ( {\it \_C1}-{\frac {2}{3}\int \!{\frac {h \left ( {\it \_b} \right ) }{{\it \_b}\, \left ( {\it \_b}-1 \right ) } \left ( {{\it \_b}}^{2}-{\it \_b} \right ) ^{-{\frac {4}{3}}}}\,{\rm d}{\it \_b}} \right ) }}}}{d{\it \_b}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!{\frac {\sqrt {9}}{3}{\frac {1}{\sqrt { \left ( {\it \_b}-1 \right ) \sqrt [3]{{\it \_b}\, \left ( {\it \_b}-1 \right ) }{\it \_b}\, \left ( {\it \_C1}-{\frac {2}{3}\int \!{\frac {h \left ( {\it \_b} \right ) }{{\it \_b}\, \left ( {\it \_b}-1 \right ) } \left ( {{\it \_b}}^{2}-{\it \_b} \right ) ^{-{\frac {4}{3}}}}\,{\rm d}{\it \_b}} \right ) }}}}{d{\it \_b}}-x-{\it \_C2}=0 \right \} \]