\[ y'(x) (a y(x)+b x+c)+\alpha y(x)+\beta x+\gamma =0 \] ✓ Mathematica : cpu = 3.80824 (sec), leaf count = 252
\[\text {Solve}\left [\frac {(\alpha -b)^2 \left (-\log \left (\frac {(a y(x)+b x+c)^2 \left (-\frac {(\alpha (b x+c)-a (\beta x+\gamma )) \left (a (\alpha -b) y(x)+a (\beta x+\gamma )+b^2 (-x)-b c\right )}{(a y(x)+b x+c)^2}+a \beta -\alpha b\right )}{(\alpha (b x+c)-a (\beta x+\gamma ))^2}\right )-\frac {2 \tan ^{-1}\left (\frac {\frac {2 a (\beta x+\gamma )-2 \alpha (b x+c)}{a y(x)+b x+c}+\alpha -b}{(\alpha -b) \sqrt {\frac {4 (a \beta -\alpha b)}{(\alpha -b)^2}-1}}\right )}{\sqrt {\frac {4 (a \beta -\alpha b)}{(\alpha -b)^2}-1}}\right )}{2 (a \beta -\alpha b)}=\frac {(\alpha -b)^2 \log (a (\beta x+\gamma )-\alpha (b x+c))}{a \beta -\alpha b}+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.254 (sec), leaf count = 178
\[\left \{y \left (x \right ) = \frac {\beta c -\gamma b +\frac {\left (-\alpha c +\gamma a +\left (a \beta -\alpha b \right ) x \right ) \left (\alpha +b +\sqrt {4 a \beta -\alpha ^{2}-2 \alpha b -b^{2}}\, \tan \left (\RootOf \left (2 \textit {\_Z} \alpha -2 \textit {\_Z} b +2 c_{1} \sqrt {4 a \beta -\alpha ^{2}-2 \alpha b -b^{2}}+\sqrt {4 a \beta -\alpha ^{2}-2 \alpha b -b^{2}}\, \ln \left (\frac {\left (a \beta x -\alpha b x -\alpha c +\gamma a \right )^{2} \left (\tan ^{2}\left (\textit {\_Z} \right )+1\right ) \left (4 a \beta -\alpha ^{2}-2 \alpha b -b^{2}\right )}{4 a}\right )\right )\right )\right )}{2 a}}{-a \beta +\alpha b}\right \}\]