ODE
\[ (1-y(x)) y''(x)+2 y'(x)^2=0 \] 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 = 0.299818 (sec), leaf count = 27
\[\left \{\left \{y(x)\to \frac {c_1 x-1+c_2 c_1}{c_1 (x+c_2)}\right \}\right \}\]
Maple ✓
cpu = 0.298 (sec), leaf count = 18
\[\left [y \left (x \right ) = \frac {\textit {\_C1} x +\textit {\_C2} -1}{\textit {\_C1} x +\textit {\_C2}}\right ]\] Mathematica raw input
DSolve[2*y'[x]^2 + (1 - y[x])*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (-1 + x*C[1] + C[1]*C[2])/(C[1]*(x + C[2]))}}
Maple raw input
dsolve((1-y(x))*diff(diff(y(x),x),x)+2*diff(y(x),x)^2 = 0, y(x))
Maple raw output
[y(x) = (_C1*x+_C2-1)/(_C1*x+_C2)]