ODE
\[ 3 (1-y(x)) y(x) y''(x)=2 (1-2 y(x)) y'(x)^2 \] ODE Classification
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.519327 (sec), leaf count = 51
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {3 \sqrt [3]{-((\text {$\#$1}-1) \text {$\#$1})} \, _2F_1\left (\frac {1}{3},\frac {2}{3};\frac {4}{3};1-\text {$\#$1}\right )}{\sqrt [3]{\text {$\#$1}} c_1}\& \right ][x+c_2]\right \}\right \}\]
Maple ✓
cpu = 0.277 (sec), leaf count = 41
\[\left [\frac {3 \left (-\mathrm {signum}\left (y \left (x \right )-1\right )\right )^{\frac {2}{3}} y \left (x \right )^{\frac {1}{3}} \hypergeom \left (\left [\frac {1}{3}, \frac {2}{3}\right ], \left [\frac {4}{3}\right ], y \left (x \right )\right )}{\mathrm {signum}\left (y \left (x \right )-1\right )^{\frac {2}{3}}}-\textit {\_C1} x -\textit {\_C2} = 0\right ]\] Mathematica raw input
DSolve[3*(1 - y[x])*y[x]*y''[x] == 2*(1 - 2*y[x])*y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> InverseFunction[(-3*Hypergeometric2F1[1/3, 2/3, 4/3, 1 - #1]*(-((-1 + #1)*#1))^(1/3))/(C[1]*#1^(1/3)) & ][x + C[2]]}}
Maple raw input
dsolve(3*y(x)*(1-y(x))*diff(diff(y(x),x),x) = 2*(1-2*y(x))*diff(y(x),x)^2, y(x))
Maple raw output
[3/signum(y(x)-1)^(2/3)*(-signum(y(x)-1))^(2/3)*y(x)^(1/3)*hypergeom([1/3, 2/3],[4/3],y(x))-_C1*x-_C2 = 0]