ODE No. 1699

\[ y(x) y''(x)+y'(x)^2-y'(x)=0 \] Mathematica : cpu = 0.130471 (sec), leaf count = 40

DSolve[-Derivative[1][y][x] + Derivative[1][y][x]^2 + y[x]*Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to c_1 \left (-W\left (-\frac {e^{-\frac {x}{c_1}-1-\frac {c_2}{c_1}}}{c_1}\right )\right )-c_1\right \}\right \}\] Maple : cpu = 0.987 (sec), leaf count = 33

dsolve(diff(diff(y(x),x),x)*y(x)+diff(y(x),x)^2-diff(y(x),x)=0,y(x))
 

\[y \left (x \right ) = -c_{1} \left (\LambertW \left (-\frac {{\mathrm e}^{-1} {\mathrm e}^{-\frac {c_{2}}{c_{1}}} {\mathrm e}^{-\frac {x}{c_{1}}}}{c_{1}}\right )+1\right )\]