ODE
\[ 2 (1-y(x)) y(x) y''(x)=(1-2 y(x)) y'(x)^2 \] 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 = 0.247544 (sec), leaf count = 37
\[\left \{\left \{y(x)\to \frac {1}{4} e^{-i c_1 \left (c_2+x\right )} \left (1+e^{i c_1 \left (c_2+x\right )}\right ){}^2\right \}\right \}\]
Maple ✓
cpu = 0.025 (sec), leaf count = 27
\[ \left \{ \ln \left ( -{\frac {1}{2}}+y \left ( x \right ) +\sqrt { \left ( y \left ( x \right ) \right ) ^{2}-y \left ( x \right ) } \right ) -{\it \_C1}\,x-{\it \_C2}=0 \right \} \] Mathematica raw input
DSolve[2*(1 - y[x])*y[x]*y''[x] == (1 - 2*y[x])*y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> (1 + E^(I*C[1]*(x + C[2])))^2/(4*E^(I*C[1]*(x + C[2])))}}
Maple raw input
dsolve(2*y(x)*(1-y(x))*diff(diff(y(x),x),x) = (1-2*y(x))*diff(y(x),x)^2, y(x),'implicit')
Maple raw output
ln(-1/2+y(x)+(y(x)^2-y(x))^(1/2))-_C1*x-_C2 = 0