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 = 0.43471 (sec), leaf count = 18
\[\left \{\left \{y(x)\to \cos ^2\left (\frac {1}{2} c_1 (x+c_2)\right )\right \}\right \}\]
Maple ✓
cpu = 0.881 (sec), leaf count = 35
\[\left [y \left (x \right ) = \frac {\left (4 \,{\mathrm e}^{2 \textit {\_C1} x} \textit {\_C2}^{2}+4 \,{\mathrm e}^{\textit {\_C1} x} \textit {\_C2} +1\right ) {\mathrm e}^{-\textit {\_C1} x}}{8 \textit {\_C2}}\right ]\] 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] -> Cos[(C[1]*(x + C[2]))/2]^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))
Maple raw output
[y(x) = 1/8*(4*exp(_C1*x)^2*_C2^2+4*exp(_C1*x)*_C2+1)/exp(_C1*x)/_C2]