\[ a x y(x)^2+b y(x)+c x+d+x y'(x)=0 \] ✓ Mathematica : cpu = 0.216978 (sec), leaf count = 301
\[\left \{\left \{y(x)\to -\frac {i \left (\sqrt {c} c_1 U\left (\frac {1}{2} \left (b+\frac {i \sqrt {a} d}{\sqrt {c}}\right ),b,2 i \sqrt {a} \sqrt {c} x\right )+c_1 \left (b \sqrt {c}+i \sqrt {a} d\right ) U\left (\frac {1}{2} \left (b+\frac {i \sqrt {a} d}{\sqrt {c}}+2\right ),b+1,2 i \sqrt {a} \sqrt {c} x\right )+\sqrt {c} \left (2 L_{-\frac {i \sqrt {a} d}{2 \sqrt {c}}-\frac {b}{2}-1}^b\left (2 i \sqrt {a} \sqrt {c} x\right )+L_{-\frac {b}{2}-\frac {i \sqrt {a} d}{2 \sqrt {c}}}^{b-1}\left (2 i \sqrt {a} \sqrt {c} x\right )\right )\right )}{\sqrt {a} \left (c_1 U\left (\frac {1}{2} \left (b+\frac {i \sqrt {a} d}{\sqrt {c}}\right ),b,2 i \sqrt {a} \sqrt {c} x\right )+L_{-\frac {b}{2}-\frac {i \sqrt {a} d}{2 \sqrt {c}}}^{b-1}\left (2 i \sqrt {a} \sqrt {c} x\right )\right )}\right \}\right \}\]
✓ Maple : cpu = 0.337 (sec), leaf count = 844
\[ \left \{ y \left ( x \right ) =-4\,{{c}^{2} \left ( -1/4\,{\it \_C1}\, \left ( {a}^{3}{c}^{2}{d}^{2}+{a}^{2}{b}^{2}{c}^{3}-2\, \left ( -ac \right ) ^{3/2}abcd-2\, \left ( -ac \right ) ^{5/2}bd \right ) {{\sl U}\left (1/2\,{\frac { \left ( -ac \right ) ^{3/2}d+c \left ( 2\,\sqrt {-ac}d+c \left ( b+2 \right ) \right ) a}{{c}^{2}a}},\,{\frac { \left ( -ac \right ) ^{3/2}d+ \left ( \sqrt {-ac}d+c \left ( b+1 \right ) \right ) ca}{{c}^{2}a}},\,2\,x\sqrt {-ac}\right )}+ \left ( a{c}^{3} \left ( ad-b\sqrt {-ac} \right ) {{\sl M}\left (1/2\,{\frac { \left ( -ac \right ) ^{3/2}d+c \left ( 2\,\sqrt {-ac}d+c \left ( b+2 \right ) \right ) a}{{c}^{2}a}},\,{\frac { \left ( -ac \right ) ^{3/2}d+ \left ( \sqrt {-ac}d+c \left ( b+1 \right ) \right ) ca}{{c}^{2}a}},\,2\,x\sqrt {-ac}\right )}+a{c}^{3} \left ( b\sqrt {-ac}+ad \right ) {{\sl M}\left (1/2\,{\frac { \left ( -ac \right ) ^{3/2}d+2\,adc\sqrt {-ac}+ab{c}^{2}}{{c}^{2}a}},\,{\frac { \left ( -ac \right ) ^{3/2}d+ \left ( \sqrt {-ac}d+c \left ( b+1 \right ) \right ) ca}{{c}^{2}a}},\,2\,x\sqrt {-ac}\right )}-1/2\,{{\sl U}\left (1/2\,{\frac { \left ( -ac \right ) ^{3/2}d+2\,adc\sqrt {-ac}+ab{c}^{2}}{{c}^{2}a}},\,{\frac { \left ( -ac \right ) ^{3/2}d+ \left ( \sqrt {-ac}d+c \left ( b+1 \right ) \right ) ca}{{c}^{2}a}},\,2\,x\sqrt {-ac}\right )}{\it \_C1}\, \left ( bc-\sqrt {-ac}d \right ) \right ) {c}^{2}{a}^{2} \right ) \left ( -{\it \_C1}\, \left ( {a}^{2}{b}^{2}{c}^{4}\sqrt {-ac}+2\,ac{d}^{2} \left ( -ac \right ) ^{5/2}+{d}^{2} \left ( -ac \right ) ^{7/2} \right ) {{\sl U}\left (1/2\,{\frac { \left ( -ac \right ) ^{3/2}d+c \left ( 2\,\sqrt {-ac}d+c \left ( b+2 \right ) \right ) a}{{c}^{2}a}},\,{\frac { \left ( -ac \right ) ^{3/2}d+ \left ( \sqrt {-ac}d+c \left ( b+1 \right ) \right ) ca}{{c}^{2}a}},\,2\,x\sqrt {-ac}\right )}+4\, \left ( {a}^{2}{c}^{2} \left ( \sqrt {-ac}d+bc \right ) {{\sl M}\left (1/2\,{\frac { \left ( -ac \right ) ^{3/2}d+c \left ( 2\,\sqrt {-ac}d+c \left ( b+2 \right ) \right ) a}{{c}^{2}a}},\,{\frac { \left ( -ac \right ) ^{3/2}d+ \left ( \sqrt {-ac}d+c \left ( b+1 \right ) \right ) ca}{{c}^{2}a}},\,2\,x\sqrt {-ac}\right )}+{a}^{2}{c}^{2} \left ( bc-\sqrt {-ac}d \right ) {{\sl M}\left (1/2\,{\frac { \left ( -ac \right ) ^{3/2}d+2\,adc\sqrt {-ac}+ab{c}^{2}}{{c}^{2}a}},\,{\frac { \left ( -ac \right ) ^{3/2}d+ \left ( \sqrt {-ac}d+c \left ( b+1 \right ) \right ) ca}{{c}^{2}a}},\,2\,x\sqrt {-ac}\right )}+1/2\,{{\sl U}\left (1/2\,{\frac { \left ( -ac \right ) ^{3/2}d+2\,adc\sqrt {-ac}+ab{c}^{2}}{{c}^{2}a}},\,{\frac { \left ( -ac \right ) ^{3/2}d+ \left ( \sqrt {-ac}d+c \left ( b+1 \right ) \right ) ca}{{c}^{2}a}},\,2\,x\sqrt {-ac}\right )}{\it \_C1}\, \left ( b\sqrt {-ac}+ad \right ) \right ) {c}^{4}{a}^{2} \right ) ^{-1}} \right \} \]