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 = 0.0663936 (sec), leaf count = 32
\[\left \{\left \{y(x)\to e^{c_1} W\left (e^{e^{-c_1} \left (-e^{c_1} c_1+c_2+x\right )}\right )\right \}\right \}\]
Maple ✓
cpu = 0.08 (sec), leaf count = 21
\[ \left \{ y \left ( x \right ) +{\it \_C1}\,\ln \left ( y \left ( x \right ) \right ) -x-{\it \_C2}=0,y \left ( x \right ) ={\it \_C1} \right \} \] 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),'implicit')
Maple raw output
y(x) = _C1, y(x)+_C1*ln(y(x))-x-_C2 = 0