\[ \boxed { \left ( 2\,y \left ( x \right ) +x+1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -2\,y \left ( x \right ) -x+1=0} \]
Mathematica: cpu = 0.017502 (sec), leaf count = 35 \[ \left \{\left \{y(x)\to \frac {2}{3} \left (W\left (-e^{c_1+\frac {9 x}{4}-1}\right )+1\right )+\frac {1}{2} (-x-1)\right \}\right \} \]
Maple: cpu = 0.047 (sec), leaf count = 21 \[ \left \{ y \left ( x \right ) =-{\frac {x}{2}}+{\frac {2}{3}{\it lambertW} \left ( {\frac {{{\rm e}^{-{\frac {1}{4}}}}{\it \_C1}}{4}{ {\rm e}^{{\frac {9\,x}{4}}}}} \right ) }+{\frac {1}{6}} \right \} \]