\[ (x+1) y'(x)^2-(y(x)+x) y'(x)+y(x)=0 \] ✓ Mathematica : cpu = 0.198642 (sec), leaf count = 59
\[\left \{\left \{y(x)\to -\frac {e^{c_1} \left (-2 x+e^{c_1}\right )}{2 \left (2+e^{c_1}\right )}\right \},\left \{y(x)\to -\frac {2 e^{c_1} \left (-x+2 e^{c_1}\right )}{1+2 e^{c_1}}\right \}\right \}\] ✓ Maple : cpu = 0.029 (sec), leaf count = 45
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\, \left ( {\it \_C1}\,x+{\it \_C1}-x \right ) }{{\it \_C1}-1}},y \left ( x \right ) =x+2-2\,\sqrt {1+x},y \left ( x \right ) =x+2+2\,\sqrt {1+x} \right \} \]