\[ (2 y(x)+x+1) y'(x)-2 y(x)-x+1=0 \] ✓ Mathematica : cpu = 0.0190394 (sec), leaf count = 30
\[\left \{\left \{y(x)\to \frac {1}{6} \left (4 W\left (-e^{c_1+\frac {9 x}{4}-1}\right )-3 x+1\right )\right \}\right \}\]
✓ Maple : cpu = 0.069 (sec), leaf count = 21
\[ \left \{ y \left ( x \right ) =-{\frac {x}{2}}+{\frac {2}{3}{\it lambertW} \left ( {\frac {{{\rm e}^{-{\frac {1}{4}}}}{\it \_C1}}{4}{{\rm e}^{{\frac {9\,x}{4}}}}} \right ) }+{\frac {1}{6}} \right \} \]