ODE
\[ 2 (1-y(x)) y(x) y''(x)=f(x) (1-y(x)) y(x) y'(x)+(1-2 y(x)) y'(x)^2 \] ODE Classification
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.219605 (sec), leaf count = 45
\[\left \{\left \{y(x)\to \cos ^2\left (\frac {1}{2} \left (\int _1^x-\exp \left (-\int _1^{K[3]}-\frac {1}{2} f(K[1])dK[1]\right ) c_1dK[3]+c_2\right )\right )\right \}\right \}\]
Maple ✓
cpu = 1.074 (sec), leaf count = 59
\[\left [y \left (x \right ) = \frac {\left (4 \,{\mathrm e}^{\int 2 \textit {\_C1} \,{\mathrm e}^{\int \frac {f \left (x \right )}{2}d x}d x} \textit {\_C2}^{2}+4 \,{\mathrm e}^{\textit {\_C1} \left (\int {\mathrm e}^{\frac {\left (\int f \left (x \right )d x \right )}{2}}d x \right )} \textit {\_C2} +1\right ) {\mathrm e}^{\int -\textit {\_C1} \,{\mathrm e}^{\int \frac {f \left (x \right )}{2}d x}d x}}{8 \textit {\_C2}}\right ]\] Mathematica raw input
DSolve[2*(1 - y[x])*y[x]*y''[x] == f[x]*(1 - y[x])*y[x]*y'[x] + (1 - 2*y[x])*y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> Cos[(C[2] + Inactive[Integrate][-(C[1]/E^Inactive[Integrate][-1/2*f[K[1]], {K[1], 1, K[3]}]), {K[3], 1, x}])/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)*(1-y(x))*diff(y(x),x)*f(x), y(x))
Maple raw output
[y(x) = 1/8*(4*exp(_C1*Int(exp(1/2*Int(f(x),x)),x))^2*_C2^2+4*exp(_C1*Int(exp(1/2*Int(f(x),x)),x))*_C2+1)/exp(_C1*Int(exp(1/2*Int(f(x),x)),x))/_C2]