ODE
\[ 4 (1-y(x)) y(x) y''(x)=3 (1-2 y(x)) y'(x)^2 \] 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 = 0.488391 (sec), leaf count = 51
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {4 \sqrt [4]{-((\text {$\#$1}-1) \text {$\#$1})} \, _2F_1\left (\frac {1}{4},\frac {3}{4};\frac {5}{4};1-\text {$\#$1}\right )}{\sqrt [4]{\text {$\#$1}} c_1}\& \right ][x+c_2]\right \}\right \}\]
Maple ✓
cpu = 0.256 (sec), leaf count = 41
\[\left [\frac {4 \left (-\mathrm {signum}\left (y \left (x \right )-1\right )\right )^{\frac {3}{4}} y \left (x \right )^{\frac {1}{4}} \hypergeom \left (\left [\frac {1}{4}, \frac {3}{4}\right ], \left [\frac {5}{4}\right ], y \left (x \right )\right )}{\mathrm {signum}\left (y \left (x \right )-1\right )^{\frac {3}{4}}}-\textit {\_C1} x -\textit {\_C2} = 0\right ]\] Mathematica raw input
DSolve[4*(1 - y[x])*y[x]*y''[x] == 3*(1 - 2*y[x])*y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> InverseFunction[(-4*Hypergeometric2F1[1/4, 3/4, 5/4, 1 - #1]*(-((-1 + #1)*#1))^(1/4))/(C[1]*#1^(1/4)) & ][x + C[2]]}}
Maple raw input
dsolve(4*y(x)*(1-y(x))*diff(diff(y(x),x),x) = 3*(1-2*y(x))*diff(y(x),x)^2, y(x))
Maple raw output
[4/signum(y(x)-1)^(3/4)*(-signum(y(x)-1))^(3/4)*y(x)^(1/4)*hypergeom([1/4, 3/4],[5/4],y(x))-_C1*x-_C2 = 0]