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 = 0.382423 (sec), leaf count = 18
\[\left \{\left \{y(x)\to \tanh ^2\left (\frac {1}{2} c_1 (x+c_2)\right )\right \}\right \}\]
Maple ✓
cpu = 0.446 (sec), leaf count = 15
\[\left [y \left (x \right ) = \tanh ^{2}\left (\frac {\textit {\_C1} x}{2}+\frac {\textit {\_C2}}{2}\right )\right ]\] 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] -> Tanh[(C[1]*(x + C[2]))/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))
Maple raw output
[y(x) = tanh(1/2*_C1*x+1/2*_C2)^2]