\[ -h(y(x))+(1-y(x)) y''(x)-3 (1-2 y(x)) y'(x)^2=0 \] ✓ Mathematica : cpu = 22.6098 (sec), leaf count = 164
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}} -\frac {e^{\frac {1}{2} (12-12 K[2])}}{(K[2]-1)^3 \sqrt {2 \int _1^{K[2]} -\frac {h(K[1]) \exp (-2 (6 (K[1]-1)+3 \log (K[1]-1)))}{K[1]-1} \, dK[1]+c_1}} \, dK[2]\& \right ]\left [c_2+x\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}} \frac {e^{\frac {1}{2} (12-12 K[3])}}{(K[3]-1)^3 \sqrt {2 \int _1^{K[3]} -\frac {h(K[1]) \exp (-2 (6 (K[1]-1)+3 \log (K[1]-1)))}{K[1]-1} \, dK[1]+c_1}} \, dK[3]\& \right ]\left [c_2+x\right ]\right \}\right \}\] ✓ Maple : cpu = 0.359 (sec), leaf count = 90
\[ \left \{ \int ^{y \left ( x \right ) }\!{\frac {1}{ \left ( {\it \_b}-1 \right ) ^{3} \left ( {{\rm e}^{{\it \_b}}} \right ) ^{6}}{\frac {1}{\sqrt {-2\,\int \!{\frac {h \left ( {\it \_b} \right ) }{ \left ( {{\rm e}^{{\it \_b}}} \right ) ^{12} \left ( {\it \_b}-1 \right ) ^{7}}}\,{\rm d}{\it \_b}+{\it \_C1}}}}}{d{\it \_b}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!-{\frac {1}{ \left ( {\it \_b}-1 \right ) ^{3} \left ( {{\rm e}^{{\it \_b}}} \right ) ^{6}}{\frac {1}{\sqrt {-2\,\int \!{\frac {h \left ( {\it \_b} \right ) }{ \left ( {{\rm e}^{{\it \_b}}} \right ) ^{12} \left ( {\it \_b}-1 \right ) ^{7}}}\,{\rm d}{\it \_b}+{\it \_C1}}}}}{d{\it \_b}}-x-{\it \_C2}=0 \right \} \]