ODE
\[ y(x) y''(x)+y'(x)^3-y'(x)^2=0 \] 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 = 0.325304 (sec), leaf count = 32
\[\left \{\left \{y(x)\to e^{c_1} W\left (e^{e^{-c_1} \left (x-e^{c_1} c_1+c_2\right )}\right )\right \}\right \}\]
Maple ✓
cpu = 1.422 (sec), leaf count = 40
\[\left [y \left (x \right ) = \textit {\_C1}, y \left (x \right ) = {\mathrm e}^{-\frac {\textit {\_C1} \LambertW \left (\frac {{\mathrm e}^{\frac {x}{\textit {\_C1}}} {\mathrm e}^{\frac {\textit {\_C2}}{\textit {\_C1}}}}{\textit {\_C1}}\right )-\textit {\_C2} -x}{\textit {\_C1}}}\right ]\] Mathematica raw input
DSolve[-y'[x]^2 + y'[x]^3 + y[x]*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^C[1]*ProductLog[E^((x - E^C[1]*C[1] + C[2])/E^C[1])]}}
Maple raw input
dsolve(y(x)*diff(diff(y(x),x),x)+diff(y(x),x)^3-diff(y(x),x)^2 = 0, y(x))
Maple raw output
[y(x) = _C1, y(x) = exp(-(_C1*LambertW(1/_C1*exp(x/_C1)*exp(1/_C1*_C2))-_C2-x)/_C1)]