ODE
\[ 2 (1-y(x)) y(x) y''(x)=(1-3 y(x)) y'(x)^2 \] 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 = 0.113353 (sec), leaf count = 32
\[\left \{\left \{y(x)\to \frac {\left (e^{c_1 \left (c_2+x\right )}-1\right ){}^2}{\left (e^{c_1 \left (c_2+x\right )}+1\right ){}^2}\right \}\right \}\]
Maple ✓
cpu = 0.054 (sec), leaf count = 18
\[ \left \{ -2\,{\it Artanh} \left ( \sqrt {y \left ( x \right ) } \right ) -{\it \_C1}\,x-{\it \_C2}=0 \right \} \] Mathematica raw input
DSolve[2*(1 - y[x])*y[x]*y''[x] == (1 - 3*y[x])*y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> (-1 + E^(C[1]*(x + C[2])))^2/(1 + E^(C[1]*(x + C[2])))^2}}
Maple raw input
dsolve(2*y(x)*(1-y(x))*diff(diff(y(x),x),x) = (1-3*y(x))*diff(y(x),x)^2, y(x),'implicit')
Maple raw output
-2*arctanh(y(x)^(1/2))-_C1*x-_C2 = 0