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 = 0.0591286 (sec), leaf count = 26
\[\left \{\left \{y(x)\to \frac {c_2+x}{W\left (e^{-c_1-1} \left (c_2+x\right )\right )}\right \}\right \}\]
Maple ✓
cpu = 0.197 (sec), leaf count = 26
\[ \left \{ y \left ( x \right ) \ln \left ( y \left ( x \right ) \right ) + \left ( {\it \_C1}-1 \right ) y \left ( x \right ) -x-{\it \_C2}=0,y \left ( x \right ) ={\it \_C1} \right \} \] 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),'implicit')
Maple raw output
y(x) = _C1, y(x)*ln(y(x))+(_C1-1)*y(x)-x-_C2 = 0