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 = 0.0388741 (sec), leaf count = 32
\[\left \{\left \{y(x)\to -c_1 \left (W\left (-\frac {e^{-\frac {c_1+c_2+x}{c_1}}}{c_1}\right )+1\right )\right \}\right \}\]
Maple ✓
cpu = 0.065 (sec), leaf count = 20
\[ \left \{ y \left ( x \right ) -{\it \_C1}\,\ln \left ( y \left ( x \right ) +{\it \_C1} \right ) -x-{\it \_C2}=0 \right \} \] 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),'implicit')
Maple raw output
y(x)-_C1*ln(y(x)+_C1)-x-_C2 = 0