ODE
\[ y(x) y''(x)+y'(x)^2=y'(x) \] ODE Classification
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.309314 (sec), leaf count = 32
\[\left \{\left \{y(x)\to -c_1 \left (1+W\left (-\frac {e^{-\frac {x+c_1+c_2}{c_1}}}{c_1}\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.93 (sec), leaf count = 33
\[\left [y \left (x \right ) = -\textit {\_C1} \left (\LambertW \left (-\frac {{\mathrm e}^{-1} {\mathrm e}^{-\frac {\textit {\_C2}}{\textit {\_C1}}} {\mathrm e}^{-\frac {x}{\textit {\_C1}}}}{\textit {\_C1}}\right )+1\right )\right ]\] Mathematica raw input
DSolve[y'[x]^2 + y[x]*y''[x] == y'[x],y[x],x]
Mathematica raw output
{{y[x] -> -(C[1]*(1 + ProductLog[-(1/(E^((x + C[1] + C[2])/C[1])*C[1]))]))}}
Maple raw input
dsolve(y(x)*diff(diff(y(x),x),x)+diff(y(x),x)^2 = diff(y(x),x), y(x))
Maple raw output
[y(x) = -_C1*(LambertW(-1/_C1*exp(-1)/exp(1/_C1*_C2)/exp(x/_C1))+1)]