\[ h(y(x))-(1-3 y(x)) y'(x)^2+2 (1-y(x)) y(x) y''(x)=0 \] ✓ Mathematica : cpu = 0.84065 (sec), leaf count = 170
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}-\frac {1}{(K[2]-1) \sqrt {K[2]} \sqrt {c_1+2 \int _1^{K[2]}\frac {e^{-2 \left (\log (1-K[1])+\frac {1}{2} \log (K[1])\right )} h(K[1])}{2 (K[1]-1) K[1]}dK[1]}}dK[2]\& \right ][x+c_2]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[3]-1) \sqrt {K[3]} \sqrt {c_1+2 \int _1^{K[3]}\frac {e^{-2 \left (\log (1-K[1])+\frac {1}{2} \log (K[1])\right )} h(K[1])}{2 (K[1]-1) K[1]}dK[1]}}dK[3]\& \right ][x+c_2]\right \}\right \}\] ✓ Maple : cpu = 1.471 (sec), leaf count = 80
\[ \left \{ \int ^{y \left ( x \right ) }\!{\frac {1}{{\it \_b}-1}{\frac {1}{\sqrt {{\it \_b}\, \left ( {\it \_C1}+\int \!{\frac {h \left ( {\it \_b} \right ) }{ \left ( {\it \_b}-1 \right ) ^{3}{{\it \_b}}^{2}}}\,{\rm d}{\it \_b} \right ) }}}}{d{\it \_b}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!-{\frac {1}{{\it \_b}-1}{\frac {1}{\sqrt {{\it \_b}\, \left ( {\it \_C1}+\int \!{\frac {h \left ( {\it \_b} \right ) }{ \left ( {\it \_b}-1 \right ) ^{3}{{\it \_b}}^{2}}}\,{\rm d}{\it \_b} \right ) }}}}{d{\it \_b}}-x-{\it \_C2}=0 \right \} \]