\[ h(y(x))+2 (1-y(x)) y(x) y''(x)-(1-3 y(x)) y'(x)^2=0 \] ✗ Mathematica : cpu = 100.24 (sec), leaf count = 0 , could not solve
DSolve[h[y[x]] - (1 - 3*y[x])*Derivative[1][y][x]^2 + 2*(1 - y[x])*y[x]*Derivative[2][y][x] == 0, y[x], x]
✓ Maple : cpu = 0.278 (sec), leaf count = 84
\[ \left \{ \int ^{y \left ( x \right ) }\!{\frac {1}{-1+{\it \_b}}{\frac {1}{\sqrt {{\it \_b}\,\int \!{\frac {h \left ( {\it \_b} \right ) }{ \left ( -1+{\it \_b} \right ) ^{3}{{\it \_b}}^{2}}}\,{\rm d}{\it \_b}+{\it \_C1}\,{\it \_b}}}}}{d{\it \_b}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!-{\frac {1}{-1+{\it \_b}}{\frac {1}{\sqrt {{\it \_b}\,\int \!{\frac {h \left ( {\it \_b} \right ) }{ \left ( -1+{\it \_b} \right ) ^{3}{{\it \_b}}^{2}}}\,{\rm d}{\it \_b}+{\it \_C1}\,{\it \_b}}}}}{d{\it \_b}}-x-{\it \_C2}=0 \right \} \]