\[ \boxed { \left ( ay \left ( x \right ) +bx+c \right ) ^{2}{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( \alpha \,y \left ( x \right ) +\beta \,x+\gamma \right ) ^{2}=0} \]
Mathematica: cpu = 54.667442 (sec), leaf count = 760 \[ \text {Solve}\left [(\alpha b-a \beta ) \text {RootSum}\left [\text {$\#$1}^3 a \beta ^3-\text {$\#$1}^3 \alpha b \beta ^2+2 \text {$\#$1}^2 a \alpha \beta ^2 y(x)+\text {$\#$1}^2 a b^2 \beta y(x)+3 \gamma \text {$\#$1}^2 a \beta ^2-2 \text {$\#$1}^2 \alpha ^2 b \beta y(x)-\text {$\#$1}^2 \alpha b^3 y(x)-2 \gamma \text {$\#$1}^2 \alpha b \beta -\text {$\#$1}^2 \alpha \beta ^2 c-\gamma \text {$\#$1}^2 b^3+\text {$\#$1}^2 b^2 \beta c+2 \text {$\#$1} a^2 b \beta y(x)^2+\text {$\#$1} a \alpha ^2 \beta y(x)^2-2 \text {$\#$1} a \alpha b^2 y(x)^2+4 \gamma \text {$\#$1} a \alpha \beta y(x)-2 \gamma \text {$\#$1} a b^2 y(x)+4 \text {$\#$1} a b \beta c y(x)+3 \gamma ^2 \text {$\#$1} a \beta -\text {$\#$1} \alpha ^3 b y(x)^2-2 \gamma \text {$\#$1} \alpha ^2 b y(x)-2 \text {$\#$1} \alpha ^2 \beta c y(x)-2 \text {$\#$1} \alpha b^2 c y(x)-\gamma ^2 \text {$\#$1} \alpha b-2 \gamma \text {$\#$1} \alpha \beta c-2 \gamma \text {$\#$1} b^2 c+2 \text {$\#$1} b \beta c^2+a^3 \beta y(x)^3-a^2 \alpha b y(x)^3-\gamma a^2 b y(x)^2+3 a^2 \beta c y(x)^2+\gamma a \alpha ^2 y(x)^2-2 a \alpha b c y(x)^2+2 \gamma ^2 a \alpha y(x)-2 \gamma a b c y(x)+3 a \beta c^2 y(x)+\gamma ^3 a+\alpha ^3 (-c) y(x)^2-2 \gamma \alpha ^2 c y(x)-\alpha b c^2 y(x)-\gamma ^2 \alpha c-\gamma b c^2+\beta c^3\& ,\frac {\text {$\#$1}^2 \beta ^2 \log (x-\text {$\#$1})+\alpha ^2 y(x)^2 \log (x-\text {$\#$1})+2 \text {$\#$1} \alpha \beta y(x) \log (x-\text {$\#$1})+2 \gamma \alpha y(x) \log (x-\text {$\#$1})+2 \gamma \text {$\#$1} \beta \log (x-\text {$\#$1})+\gamma ^2 \log (x-\text {$\#$1})}{-3 \text {$\#$1}^2 a \beta ^3+3 \text {$\#$1}^2 \alpha b \beta ^2-4 \text {$\#$1} a \alpha \beta ^2 y(x)-2 \text {$\#$1} a b^2 \beta y(x)-6 \gamma \text {$\#$1} a \beta ^2+4 \text {$\#$1} \alpha ^2 b \beta y(x)+2 \text {$\#$1} \alpha b^3 y(x)+4 \gamma \text {$\#$1} \alpha b \beta +2 \text {$\#$1} \alpha \beta ^2 c+2 \gamma \text {$\#$1} b^3-2 \text {$\#$1} b^2 \beta c-2 a^2 b \beta y(x)^2-a \alpha ^2 \beta y(x)^2+2 a \alpha b^2 y(x)^2-4 \gamma a \alpha \beta y(x)+2 \gamma a b^2 y(x)-4 a b \beta c y(x)-3 \gamma ^2 a \beta +\alpha ^3 b y(x)^2+2 \gamma \alpha ^2 b y(x)+2 \alpha ^2 \beta c y(x)+2 \alpha b^2 c y(x)+\gamma ^2 \alpha b+2 \gamma \alpha \beta c+2 \gamma b^2 c-2 b \beta c^2}\& \right ]=c_1,y(x)\right ] \]
Maple: cpu = 0.031 (sec), leaf count = 124 \[ \left \{ y \left ( x \right ) ={\frac {1}{-a\beta +b\alpha } \left ( - \gamma \,b+\beta \,c+{\it RootOf} \left ( \int ^{{\it \_Z}}\!{\frac {{{ \it \_a}}^{2}{a}^{2}-2\,{\it \_a}\,ab+{b}^{2}}{{{\it \_a}}^{3}{a}^{2}- 2\,{{\it \_a}}^{2}ab-{{\it \_a}}^{2}{\alpha }^{2}+2\,{\it \_a}\,\alpha \,\beta +{\it \_a}\,{b}^{2}-{\beta }^{2}}}{d{\it \_a}}+\ln \left ( ax \beta -\alpha \,bx+a\gamma -\alpha \,c \right ) +{\it \_C1} \right ) \left ( x \left ( a\beta -b\alpha \right ) +a\gamma -\alpha \,c \right ) \right ) } \right \} \]