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 = 0.319485 (sec), leaf count = 53
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\frac {4 (1-\text {$\#$1})^{3/4} \text {$\#$1} \, _2F_1\left (\frac {1}{4},\frac {3}{4};\frac {5}{4};\text {$\#$1}\right )}{(-(\text {$\#$1}-1) \text {$\#$1})^{3/4} c_1}\& \right ]\left [c_2+x\right ]\right \}\right \}\]
Maple ✓
cpu = 0.046 (sec), leaf count = 41
\[ \left \{ 4\,{\frac { \left ( -{\it signum} \left ( y \left ( x \right ) -1 \right ) \right ) ^{3/4}\sqrt [4]{y \left ( x \right ) }{\mbox {$_2$F$_1$}(1/4,3/4;\,5/4;\,y \left ( x \right ) )}}{ \left ( {\it signum} \left ( y \left ( x \right ) -1 \right ) \right ) ^{3/4}}}-{\it \_C1}\,x-{\it \_C2}=0 \right \} \] 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)^(3/4)*#1)/(C[1]*(-((-1 + #1)*#1))^(3/4)) & ][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),'implicit')
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