ODE
\[ y(x) y''(x)+y'(x)^3=0 \] ODE Classification
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.310285 (sec), leaf count = 26
\[\left \{\left \{y(x)\to \frac {x+c_2}{W\left (e^{-1-c_1} (x+c_2)\right )}\right \}\right \}\]
Maple ✓
cpu = 1.055 (sec), leaf count = 23
\[[y \left (x \right ) = \textit {\_C1}, y \left (x \right ) = {\mathrm e}^{\LambertW \left (\left (x +\textit {\_C2} \right ) {\mathrm e}^{\textit {\_C1}} {\mathrm e}^{-1}\right )-\textit {\_C1} +1}]\] Mathematica raw input
DSolve[y'[x]^3 + y[x]*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (x + C[2])/ProductLog[E^(-1 - C[1])*(x + C[2])]}}
Maple raw input
dsolve(y(x)*diff(diff(y(x),x),x)+diff(y(x),x)^3 = 0, y(x))
Maple raw output
[y(x) = _C1, y(x) = exp(LambertW((x+_C2)*exp(_C1)*exp(-1))-_C1+1)]